Properties of Triangle Centers Worksheets

Document Sample
Properties of Triangle Centers Worksheets Powered By Docstoc
					                                                           CURRICULUM MAP: GEOMETRY REGENTS
                                                                              RCSD- Department of Mathematics
                                                                                       2010 - 2011

 Pacing      Unit/Essential Questions            Essential Knowledge-
                                            Content/Performance Indicators                   Essential Skills                    Vocabulary                        Resources
                                              (What students must learn)             (What students will be able to do)

           Unit of Review               Student will review:
                                        A.A.19 Identify and factor the difference
                                                                                     Students will review:                 quadratic function
9/2-9/10                                      of two squares                          1. Solve multi-step                  quadratic equation
           1. How do you solve
                                        A.A.20 Factor algebraic expressions
                                                                                         equations (including
                                                                                                                           linear function                        JMAP
6 days     equations with                      completely, including trinomials                                            linear equation        A.A.19, A.A.20, A.A.22, A.A.25, A.A.27
           fractions using inverse             with a lead coefficient of one
                                              (after factoring a GCF)
                                                                                      2. Factoring all types.
                                                                                                                           system of equations    A.A.28, A.G.4 A.G.8
           operations or using the                                                    3. Graph quadratic functions         parabola
           LCD to clear                 A.A.22 Solve all types of linear                 and solve quadratic
                                                                                                                           algebraic expression     
                                              equations in one variable.                 equations algebraically and
           denominators in the                                                           graphically.                      monomial               Solving Fractional Equations
           equation?                    A.A.25 Solve equations involving
                                                                                                                           binomial               Linear Equations
                                               fractional expressions. Note:          4. Solve systems of linear &
                                               Expressions which result in               quadratic equations               trinomial              Factoring
           2. How do you factor                linear equations in one variable          graphically & algebraically.                              Quadratic Equations
                                                                                                                           polynomial
           algebraic expressions?                                                                                                                  Graphing Parabolas
                                        A.A.27 Understand and apply the                                                    coefficient
                                               multiplication property of zero
                                               to solve quadratic equations                                                GCF
           3. How do you solve
           quadratic equations
                                               with integral coefficients and                                              multiplication
                                               integral roots
           graphically and                                                                                                  property of zero
                                        A.A.28 Understand the difference and                                               factor
                                               connection between roots of a
                                               quadratic equation and factors of a
                                               quadratic expression.

                                        A.G.4 Identify and graph quadratic

                                        A.G.8 Find the roots of a parabolic
                                              function graphically.
                                 Students will learn:                     Students will be able to:            undefined term                        Holt Text
9/13-         Chapter 1          G.G.17 Construct a bisector of a given    1. identify, name and draw          point                1-1: pg 6-8 (Examples 1-4)
9/22        Foundations of              angle, using a straightedge and
                                        compass, and justify the
                                                                              points, lines, segments, rays
                                                                              and planes
                                                                                                               line                 1-2: pg 13-16 (Examples 1-5, include
              Geometry                  construction                                                           plane                     constructions)
8 days
                                 G.G.66 Find the midpoint of a line
                                                                           2. use midpoints of segments to
                                                                              find lengths
                                                                                                               collinear            1-3: pg 20-24 (Examples 1-4, include
         What are the building          segment, given its endpoints                                           coplanar                  constructions)
         blocks of geometry                                                3. construct midpoints and
                                                                                                               segment              1-4: pg 28-30 (Examples 1-5)
                                 G.G.67 Find the length of a line             congruent segments
         and what symbols do           segment, given its endpoints                                            endpoint             1-5: pg 36-37 (Examples 1-3)
         we use to describe                                                4. use definition of vertical.
                                                                                                               ray                  1-6: pg 43-46 (Examples1-4)
                                                                              complementary and
         them?                                                                supplementary angles to find     opposite rays
                                                                              missing angles
                                                                                                               postulate                 Geometry Labs from Holt Text
                                                                                                                                     1-1 Exploration
                                                                           5. apply formulas for perimeter,    coordinate
                                                                              area and circumference                                 1-3 Exploration
                                                                                                               distance             1-3 Additional Geometry Lab
                                                                           6. use midpoint and distance        length               1-4 Exploration
                                                                              formulas to solve problems
                                                                                                               congruent segments   1-5 Exploration
                                                                                                               construction         1-5 Geometry Lab 1
                                                                                                               between              1-5 Geometry Lab 2
                                                                                                               midpoint             1-6 Exploration
                                                                                                               bisect
                                                                                                               segment bisector
                                                                                                               adjacent angles                GSP Labs from Holt
                                                                                                               linear pair          1-2 Exploration
                                                                                                               complementary        1-2 Tech Lab p. 12
                                                                                                                angles               pg. 27: Using Technology
                                                                                                               supplementary
                                                                                                                angles                     Vocab Graphic Organizers
                                                                                                               vertical angles      1-1 know it notes 1-4 know it notes
                                                                                                               coordinate plane     1-2 know it notes 1-5 know it notes
                                                                                                               leg                  1-3 know it notes 1-6 know it notes
                                                                                                               hypotenuse                            JMAP
                                                                                                                                            G.G.17, G.G.66, G.G.67
 Lines and Planes
 Finding Distances
Reasoning with Rules
              Chapter 2:          G.G.24 Determine the negation of a
                                         statement and establish its truth
                                                                             1. Student will identify, write, and
                                                                                analyze the truth value of
                                                                                                                       Inductive reasoning                     Holt Text
9/23-         Geometric                  value                                  conditional statements.                Conjecture            2-1: pg 74-79
10/1          Reasoning
                                  G.G.25 Know and apply the conditions       2. Students will write the inverse,
                                                                                                                       Counterexample        2-2: pg 81-87
                                         under which a compound                 converse, and contrapositive of a      Conditional           2-4: pg 96-101
7 days   1. How is logical               statement (conjunction,                conditional statement.
                                                                                                                            statement         Pg 128-129
                                         disjunction, conditional,
         reasoning used in               biconditional) is true.             3. Students will write and analyze        Hypothesis            2-5: 104-109
                                  G.G.26 Identify and write the inverse,
                                                                                biconditional statements.
                                                                                                                       Conclusion            2-6: pg 110-116
                                         converse, and contrapositive of a   4. Students will analyze the truth        Truth table           2-7: pg 118-125
         2. How is reasoning             given conditional statement and        value of conjuctions and
                                                                                                                       Negation
                                         note the logical equivalences.         disjunctions.
         used to construct a                                                                                           Converse               Vocabulary development – Graphing
         formal algebraic         G.G. 27 Write a proof arguing from a       5. Students will identify properties
                                                                                                                       Inverse                              Organizers
                                         given hypothesis to a given            of equality and congruency.
         proof?                                                                                                                               2-2: graphing organizer
                                         conclusion                                                                    Contrapositive
                                                                             6. Students will write two column                                2-4: graphing organizer
                                                                                proofs.                                Biconditional
         3. How can angle                                                                                                                     2-5: know it notes
         relationships be                                                                                                                     2-6: know it notes
                                                                                                                       Compound statement
         identified, solved and
         proved?                                                                                                       Conjuction
                                                                                                                       Disjunction           G.G.24, G.G.25, G.G.26
                                                                                                                       proof
                                                                                                                                              Related Conditionals
                                                                                                                                              Writing proofs
                                   G.G.18 Construct the perpendicular
                                          bisector of a given segment, using
                                                                                 1. construct the perpendicular
                                                                                    bisector of a segment
                                                                                                                         parallel lines                             Holt Text
10/4-         Chapter 3                   a straightedge and compass, and                                                perpendicular lines             Be sure to include proofs and
10/18        Parallel and                 justify the construction               2. construct parallel or
                                                                                    perpendicular lines to a given
                                                                                                                         skew lines                     constructions throughout unit.
          Perpendicular Lines      G.G.19 Construct lines parallel (or              line and point                       parallel planes          3-1: pg. 146-147 (Examples 1-3)
10 days                                   perpendicular) to a given line
                                          through a given point, using a         3. identify and explore special
                                                                                                                         transversal              3-2 : pg. 155-157 (Examples 1-3)
                                          straightedge and compass, and             angle relationships formed           corresponding angles     Geometry Lab: pg. 170 Activity 1
          What special                    justify the construction                  when two parallel lines are cut
                                                                                                                         alternate interior                        Constructing Parallel Lines
                                                                                    by a transversal
          relationships exist in   G.G.35 Determine if two lines cut by a                                                 angles                   3-4: pg. 172-74 (Theorems p.173)
          parallel and                    transversal are parallel, based on     4. determine when two lines that
                                                                                                                         alternate exterior                 Be sure to include construction of
                                          the measure of given pairs of             are cut by a transversal are
          perpendicular lines?            angles formed by the transversal          parallel based on given angle         angles                             perpendicular bisector
                                          and the lines                             measures
                                                                                                                         same side interior       Geometry Lab: pg. 179 Constructing
                                   G.G. 62 Find the slope of a perpendicular                                              angles                                    perpendicular lines through
                                           line, given the equation of a line    5. explore relationships of slopes
                                                                                                                         bisector                                  a given point
                                                                                    to determine when two lines
                                                                                                                                                   3-5: pg 182-184 (Examples 1-3)
                                   G.G.63 Determine whether two lines are           are parallel, perpendicular or       perpendicular bisector
                                                                                                                                                   3-6 : pg 190-193 (Examples 1-3)
                                           parallel, perpendicular or neither,
                                           given their equations
                                                                                                                         distance from a point
                                                                                                                                                          Be sure to include exercises on pg.
                                                                                                                          to a line
                                                                                                                                                          195 #41- 44 and #47-51
                                   G.G.64 Find the equation of a line, given a
                                            point on the line and the equation
                                                                                 6. write the equations of lines that
                                                                                    are parallel or perpendicular to     slope                    (Note: Students can write equation of line
                                            of a line perpendicular to the          a given line that pass through a     positive slope            in any form. They will not be told to
                                            given line                              specific point
                                                                                                                         negative slope            write it in point slope form or slope
                                   G.G.65 Find the equation of a line, given     7. solve quadratic-linear               zero slope                intercept form.)
                                          a point on the line and the               systems graphically
                                          equation of a line parallel to the                                             undefined slope
                                          desired line                                                                   x-intercept              p. 199 Solving quad-linear systems
                                   G.G.68 Find the equation of a line that is                                            y-intercept                     graphically
                                          the perpendicular bisector of a                                                linear functions
                                          line segment, given the endpoints
                                          of the line segment.                                                           point slope form              Geometry Labs from Holt Text
                                   G.G.70 Solve systems of equations
                                                                                                                         slope-intercept form     3-1 Exploration
                                          involving one linear equation                                                  vertical line            3-2 Exploration
                                          and one quadratic equation
                                                                                                                         horizontal line          3-2 Additional Geometry Lab
                                                                                                                                                   3-3 Geometry Lab p. 170
                                                                                                                                                   3-4 Exploration
                                                                                                                                                   3-4 Geometry Lab p. 179
3-4 Geoboard Geometry Lab
3-5 Exploration
3-5 Geoboard Geometry Lab
3-6 Exploration
3-6 Tech Lab p. 188
3-6 B Additional Lab

          GSP Labs from Holt
3-2 Tech Lab p. 154
3-3 Exploration

       Vocab Graphic Organizers
3-1: know it notes 3-4: know it notes
3-2: know it notes 3-5: know it notes
3-3: know it notes 3-6: know it notes


Constructions, Parallel Lines,
Slopes and Equations of Lines,
Linear and Quadratic Systems, Equations
of Lines Review

        Slopes of Lines Activity
     GSP: Angles & Parallel Lines
       Slope Demo with SkiBird
    Math in the Movies- October Sky
                                    G.G.27    Write a proof arguing from a        1. classify triangles by angle
                                                                                                                         acute triangle                         Holt Text
10/19-                                        given hypothesis to a given            measures and side lengths.          equiangular triangle         Be sure to include proofs and
11/12          Chapter 4                      conclusion
                                                                                  2. find the measures of interior
                                                                                                                         right triangle              constructions throughout unit.
          Triangle Congruency       G.G. 28 Determine the congruence of two          and exterior angles of triangles    obtuse triangle
17 days                                     triangles by using one of the five
                                            congruence techniques                 3. use congruent triangles to
                                                                                                                         equilateral triangle    4-1: pg 216-221 (Examples 1-4)
          1. What types of                  (SSS,SAS,ASA,AAS, HL), given             identify corresponding parts        isosceles triangle      4-2: pg 223-230 (Examples 1-4)
          triangles are there and           sufficient information about the
                                                                                                                         scalene triangle        4-3: pg 231 – 237 (Examples 1-4)
                                            sides and/or angles of two            4. determine when two triangles
          what are some                     congruent triangles                      are congruent by SSS ,SAS,          interior angle of a     4-4: pg 242-246 (Examples 1-4)
          properties that are                                                        ASA, AAS and HL
                                                                                                                          triangle                4-5: pg 252 -259 (Examples 1-4)
                                    G.G.29 Identify corresponding parts of
          unique to them?                  congruent triangles                    5. use coordinate geometry to          exterior angle of a     4-6: pg 260-262 (Examples 1-4)
                                                                                     justify and investigate
                                                                                                                          triangle                4-7: pg 267 – 272 (Examples 1-4)
                                    G.G.30 Investigate, justify and apply            properties of triangles
          2. What postulates are           theorems about the sum of the                                                 remote interior angle   4-8: pg 273 -278 (Examples 1-4)
          used to prove triangle                                                                                                                  Extension pg 282-283
                                           measures of the angles of a
                                           triangle                                                                      congruent polygons
                                                                                                                         congruent triangles
                                    G.G.31 Investigate, justify and apply the                                                                          Geometry Labs from Holt Text
                                           isosceles triangle theorem and its                                            corresponding angles    4-1 Exploration
                                           converse.                                                                     corresponding sides     4-2 Geometry Lab p. 222
                                    G.G.36 Investigate, justify and apply                                                included angle          4-2 Additional Tech Lab
                                           theorems about the sum of the                                                 included side           4-3 Exploration
                                           measures of the interior and
                                           exterior angles of polygons                                                   legs of an isosceles    4-4 Exploration
                                                                                                                          triangle                4-4 Geometry Lab p.240
                                    G.G.37 Investigate, justify and apply
                                            theorems about each interior and                                             base angles of an       4-4 Additional Geometry Lab
                                           exterior angle measure of regular                                              isosceles triangle      4-5 Exploration
                                                                                                                         vertex angle of an      4-6 Exploration
                                    G.G.69 Investigate, justify and apply the                                             isosceles triangle      4-7 Exploration
                                            properties of triangles and
                                            quadrilaterals in the coordinate                                                                      4-8 Exploration
                                            plane, using the distance, midpoint
                                            and slope formulas
                                                                                                                                                            GSP Labs from Holt
                                                                                                                                                  4-2 Exploration
                                                                                                                                                  4-4 bottom of p.249
                                                                                                                                                  4-5 Tech Lab p. 250

                                                                                                                                                         Vocab Graphic Organizers
                                                                                                                                                  4-1: know it notes 4-5: know it notes
4-2: know it notes 4-6: know it notes
4-3: know it notes 4-7: know it notes
4-4: know it notes 4-8: know it notes


 Proper Notation: Congruence vs Equality
 Basic Vocab for Formal Proofs
 Vocabulary Matching
 Triangle Congruency,
Angles and Triangles,
Isosceles Triangle Theorems,
Coordinate Geometry Proofs for Triangle
Triangle Regents Questions
         Review                  G.G.17 Construct a bisector of a given
                                        angle, using a straightedge and
                                                                             1. Students will construct a
                                                                                bisector of a given angle.
                                                                                                                        Construct                       JMAP
11/15-   Constructions                  compass, and justify the                                                        Bisector        G.G.17, G.G.18, G.G.19, G.G.20
11/17                                   construction                         2. Students will construct the
                                                                                perpendicular bisector of a
                                                                                                                        Parallel
         What geometric          G.G.18 Construct the perpendicular             given segment                           Perpendicular      
3 days   conclusions can be             bisector of a given segment, using
                                        a straightedge and compass, and      3. Students will construct lines
                                                                                                                        Equilateral     Bisect a line segment and an angle
         drawn from using               justify the construction                parallel to a given line through a                       Parallel through a point
         constructions as your                                                  given point                                              Perpendiculars
                                 G.G.19 Construct lines parallel (or
         hypothesis?                    perpendicular) to a given line       4. Students will construct lines                            Equilateral triangle
                                        through a given point, using a          perpendicular to a given line
                                        straightedge and compass, and           through a given point
                                        justify the construction                                                                                    Other Resources
                                                                             5. Students will construct an                                     SEE ATTACHED PACKET
                                 G.G.20 Construct an equilateral triangle,      equilateral triangle
                                        using a straightedge and compass,
                                        and justify the construction         6. Students will justify the
                                   G.G.21 Investigate and apply the             1. list angles of a triangle in order
                                                                                                                         equidistant                             Holt Text
              Chapter 5                   concurrence of medians, altitudes,       from smallest to largest when         locus                    5-1 pg. 300-303 (Examples 1-4)
11/18-      Relationships in              angle bisectors and perpendicular
                                          bisectors of triangles.
                                                                                                                         concurrent               5-2 pg. 307-310 (Examples 1-4)
12/10          Triangles                                                        2. the lengths of sides of a triangle    point of concurrency     5-3 pg. 314-316 (Examples 1-3)
                                   G.G.32 Investigate, justify and apply
                                          theorems about geometric              3. list sides of a triangle in order
                                                                                                                         circumcenter of          5-4 pg. 322-323 (Examples 1-3)
14 days                                   inequalities, using the exterior         from smallest to largest when          triangle                 5-5 pg. 332-334 (Examples 1-5)
                                          angle theorem                            given two angles of a triangle
                                                                                                                         circumscribed            Review Simplest Radical Form pg 346
          1. What properties are                                                4. determine whether three given         incenter                 5-7 pg. 348-352 (Examples 1-4)
          unique to the various    G.G.33 Investigate, justify and apply           side lengths can form a triangle
                                                                                                                         inscribed
                                          the triangle inequality theorem
          centers of a triangle?                                                5. find the missing side length of       median of a triangle          Geometry Labs from Holt Text
                                                                                   a right triangle when given the
                                                                                                                         centroid of a triangle   5-1 Exploration
                                   G.G.34 Determine either the longest side        length of the other two sides
                                                                                                                                                   5-1 Graphing Calculator Lab
                                          of a triangle given the three angle                                            altitude of a triangle
          2. What are the                 measures or the largest angle         6. use the Pythagorean theorem to                                  5-2 Graphing Calculator Lab
                                          given the lengths of three sides of      determine when a triangle is a        orthocenter of a
          inequality                                                                                                                               5-3 Exploration
                                          a triangle                               right triangle                         triangle
          relationships in                                                                                                                         5-3 Additional Geometry Lab
                                   G.G.42 Investigate, justify and apply                                                 Euler line
          triangles?                                                                                                                               5-5 Geometry Lab p. 331
                                          theorems about geometric                                                       midsegment of a          5-7 Geometry Lab p. 347
                                          relationships, based on the
                                          properties of the line segment                                                  triangle
          3. How do we use the                                                                                                                     5-7 Additional Tech Lab
          Pythagorean theorem
                                          joining the midpoints of two sides                                             indirect proof
                                          of the triangle
          and its converse to                                                                                            Pythagorean triple                 GSP Labs from Holt
          solve problems?
                                   G.G.43 Investigate, justify and apply                                                 radical                  5-2 Exploration
                                          therems about the centroid of a
                                          triangle, dividing each median into                                            radicand                 5-3 Tech Lab p. 321
                                          segments who lengths are in the
                                          ratio 2:1
                                                                                                                         root                     5-4 Exploration
                                                                                                                                                   5-5 Exploration
                                   G.G.48 Investigate, justify and apply                                                                           5-7 Exploration
                                           the Pythagorean theorem and
                                           its converse
                                                                                                                                                         Vocab Graphic Organizers
                                   Students will review:                                                                                           5-1 know it notes 5-4 know it notes
                                   A.N.2 Simplify radicals (no variables
                                                                                                                                                   5-2 know it notes 5-5: know it notes
                                         in radicand)                                                                                              5-3 know it notes 5-7: know it notes

G.G.21, G.G.32, G.G.33,G.G.34, G.G.43

      Triangle Inequality Theorems
       Midsegment of a Triangle

        Concurrency of Triangles
Multiple Choice Triangle Centers Practice
  Pythagorean Theorem and Converse

   Math in the Movies Wizard of Oz
             Chapter 6:          G.G.27 Write a proof arguing from a
                                        given hypothesis to a given
                                                                                                                         Polygon                               Holt Text
12/13-      Quadrilaterals              conclusion                            1. Students will classify polygons         Vertex of a polygon   6-1: pg 382-388
                                 G.G.36 Investigate, justify, and apply
                                                                                 by number of sides and shape.           Diagonal              6-2: pg 390-397
             What types of              theorems about the sum of the                                                    Regular polygon       6-3: pg 398-405
15 days   quadrilaterals exist          measures of the interior and
                                        exterior angles of polygons
                                                                              2. Students will discover and apply
                                                                                 relationships between interior
                                                                                                                         Exterior angle        6-4: pg 408-415
          and what properties                                                    and exterior angles of polygons         Concave               6-5: pg 418-425
          are unique to them?    G.G.37 Investigate, justify, and apply
                                                                                                                         Convex                6-6: pg 429-435 (no kites)
                                        theorems about each interior and      3. Students will classify
                                        exterior angle measure of regular        quadrilaterals according to             Parallelogram
                                        polygons                                 properties.
                                                                                                                         Rectangle                       GSP from Holt Text
                                 G.G.38 Investigate, justify, and apply       4. Students will apply properties of       Rhombus               6-2: Exploration
                                        theorems about parallelograms                                                                           6-2: technology lab
                                        involving their angles, sides, and
                                                                                 parallelograms, rectangles,
                                                                                 rhombi, squares and trapezoids          Square
                                                                                                                                                6-5: pg 416-417
                                        diagonals                                to real-world problems                  Trapezoid
                                                                                                                                                6-6: pg 426
                                 G.G.39 Investigate, justify, and apply       5. Students will write proofs of           Base of a trapezoid
                                        theorems about special                   quadrilaterals                          Base angle of a
                                                                                                                                                     Geometry Labs from Holt Text
                                        parallelograms (rectangles,
                                        rhombuses, squares) involving         6. Students will investigate, justify       trapezoid             6-1: Exploration
                                        their angles, sides, and diagonals       and apply properties of                 Isosceles trapezoid   6-2: pg 390
                                                                                 quadrilaterals in the coordinate
                                 G.G.40 Investigate, justify, and apply          plane                                   Midsegment of a       6-3: Exploration
                                        theorems about trapezoids                                                         trapezoid
                                        (including isosceles trapezoids)                                                                        6-3: Lab with geoboard
                                        involving their angles, sides,                                                   Midpoint              6-4: Exploration
                                        medians, and diagonals                                                           Slope                 6-4: Lab with tangrams
                                 G.G.41 Justify that some quadrilaterals                                                 Distance              6-6: Lab with geoboard – no kites
                                        are parallelograms, rhombuses,
                                        rectangles, squares, or trapezoids
                                                                                                                                                      Vocab Graphing Organizers
                                 G.G.69 Investigate, justify, and apply the
                                        properties of triangles and                                                                             6-1: know it notes
                                        quadrilaterals in the coordinate                                                                        6-2: know it notes
                                        plane, using the distance,
                                        midpoint, and slope formulas
                                                                                                                                                6-3: know it notes
                                                                                                                                                6-4: know it notes
                                                                                                                                                6-5: know it notes
                                                                                                                                                6-6: know it notes – no kites

                   G.G.36, G.G.37, G.G.38, G.G.39, G.G.40,
                   G.G.41, G.G.69

                   G.G.36 and G.G.37, G.G.38-G.G.41,

                   GSP worksheets – angles in polygon
                   GSP worksheets – quadrilateral

1/18-    MIDTERM
1/24     REVIEW

5 days
               Chapter 7:            Students will learn:                          1. Students will write and simplify
                                                                                                                           Dilation                            Holt Text
1/31-           Similarity           G.G.44     Establish similarity of            2. Students will use proportions to     Proportion          7-1: pg 454-459 (Examples 1-5)
2/18         and Chapter 8:                     triangles, using the following        solve problems.
                                                                                   3. Students will identify similar
                                                                                                                           Ratio               7-2: pg 462-467 (Examples 1-3)
                                                theorems: AA, SAS, and SSS
            (section 8-1 only)                                                        polygons and apply properties        Scale               7-3: pg 470-477 (Examples 1-5)
15 days                              G.G. 45 Investigate, justify, and apply          of similar polygons to solve
                                                                                                                           Scale drawing       7-4: pg 481-487 (Examples 1-4)
          1. How do you know                  theorems about similar
                                                                                   4. Students will prove certain          Scale factor        7-5: pg 488-494 (Examples 1-3, discover
             when your                                                                triangles are similar by using
                                                                                                                           Similar                      4)
                                                                                      AA, SSS, and SAS and will use
             proportion is set up    G.G.46     Investigate, justify, and apply       triangle similarity to solve         Similar polygons    7-6: pg 495-500 (Examples 1-4)
             correctly?                         theorems about proportional                                                                     8-1: pg. 518-520 (Examples 1-4)
                                                relationships among the
                                                                                   5. Students will use properties of      Similarity ratio
          2. What are some                      segments of the sides of the          similar triangles to find segment    Side
             ways to determine                  triangle, given one or more           lengths.                                                        Vocab Graphic Organizers
                                                lines parallel to one side of a    6. Students will apply                  Angle
             of any two                                                                                                                         7-1: Know it Notes
                                                triangle and intersecting the         proportionality and triangle         Parallel
             polygons are                                                             angle bisector theorems.                                  7-2: Know it Notes
                                                other two sides of the triangle
                                                                                                                           mean proportional
             similar? Think                                                                                                                     7-3: Know it Notes
                                     G.G.47 Investigate, justify and apply         7. Students will use ratios to make      theorem
             physically and                                                           indirect measurements and use                             7-4: Know it Notes
                                             theorems about mean
                                             proportionality: the altitude to         scale drawings to solve              geometric mean      7-5: Know it Notes
                                             the hypotenuse of a right triangle       problems.
          3. How can you prove               is the mean proportional between                                                                   7-6: Know it Notes
             if triangles are                the two segments along the            8. Students will apply similarity                            8-1: Know it Notes
                                             hypotenuse; the taltitude to the         properties in the coordinate
             similar?                        hypotenuse of a right triangle           plane and use coordinate proof
          4. When you dilate a               divides the hypotenuse so that           to prove figures similar.                                           GSP from Holt Text
                                             either leg of the right triangle is
             figure, is it the               the mean proportional between
                                                                                                                                                7-2 Tech Lab p.460
             same as creating a              the hypotenuse and segment of                                                                      7-3 Tech Lab p.468
             figure similar to the           the hypotenuse adjacent to that                                                                    7-4 Exploration
             original one?                                                                                                                      7-4 Tech Lab p. 480
                                     G.G.58     Define, investigate, justify,
                                                and apply similarities                                                                               Geometry Labs from Holt Text
                                                (dilations …)                                                                                   7-1 Exploration 7-2 Exploration
                                                                                                                                                7-2 Geoboard Lab 7-3 Exploration
                                                                                                                                                7-5 Exploration 7-6 Exploration
                                                                                                                                                7-6 Geoboard lab 8-1 Exploration
                                                                                                                                                 8-1 Tech Lab with Graphing Calculator
G.G.44, G.G.45, G.G.46, G.G.47

Lesson: Midsegment Theorem
Practice: Midsegment Theorem
Teacher Resource: Discovering
Midsegment Theorem
Lesson: Similar Triangles
Lesson: Similar Figure Info
Lesson: Proofs with Similar Triangles
Lesson: Strategies for Dealing with
Similar Triangles
Practice: Similarity Numerical Problems
Practice: Similarity Proofs
Lesson: Mean Proportional In a Right
Practice: Mean Proportional in a Right
                                  G.G.1 Know and apply that if a line is
                                         perpendicular to each of two
                                                                              1. identify perpendicular lines     Point                                Holt Text
2/28-    Three-Dimensional               intersecting lines at their point    2. identify perpendicular planes    Perpendicular                G.G.1-4, 6:
3/8       Plane Geometry                 of intersection, then the line is
                                         perpendicular to the plane           3. define line, segment and ray
                                                                                                                  Coplanar                      3-4 Extension: Lines
                                         determined by them                                                       Parallel                      Perpendicular to Planes pg. NY
7 days   1. What is the                                                 4.    4. define a plane and what the      Parallel lines                180A-D
                                  G.G.2   Know and apply that through            minimum requirements are
         difference between a            a given point there passes one          for a plane (3 points)           Parallel planes
         line, a segment and             and only one plane                                                       Skewed lines                 G.G.7-10:
                                         perpendicular to a given line        5. know the differences in what
         a ray?                                                                  is formed when lines             Point of intersection         10-3 Extension: Perpendicular
                                  G.G.3    Know and apply that through a
                                           given point there passes one
                                                                                 intersect lines, planes
                                                                                 intersect planes, and lines
                                                                                                                  Line                              Planes and Parallel Planes pg.
         2. What is the                    and only one line                     intersect planes.                Ray                               NY 678A-D
         difference between                perpendicular to a given plane
                                                                              6. Understand the meaning of
                                                                                                                  Line segment
         the intersection of 2    G.G.4    Know and apply that two lines         coplanar                                                       G.G.10:
         lines, 2 planes, and a            perpendicular to the same                                                                             Chapter 10-1 Solid Geometry pg.
                                           plane are coplanar         7.      7. Understand the meaning of
         line with a plane?                                                      collinear
                                  G.G.5    Know and apply that two
                                           planes are perpendicular to 8.     8. Visualize and represent each
         3. What is formed                 each other if and only if one         of the aforementioned P.I.s
         when a plane                      plane contains a line                 that they will learn.                                     G.G.1, G.G.2, G.G.3, G.G.4, G.G.5,
                                           perpendicular to the second
         intersects 2 other                plane
                                                                                                                                              G.G.6, G.G.7, G.G.8, G.G.9
         parallel planes?                                                                                                                          Amsco Resources
                                  G.G.6    Know and apply that if a line is
                                           perpendicular to a plane, then
                                                                                                                                             Ch. 11-1: G.G.1, G.G.2, G.G.3
                                           any line perpendicular to the                                                                     Ch. 11-2: G.G.4, G.G.7, G.G.8
                                           given line at its point of
                                           intersection with the given
                                                                                                                                                    Ch. 11-3: G.G.9
                                           plane is in the given plane                                                                            Pearson Resources
                                  G.G.7    Know and apply that if a line is
                                                                                                                                                   Online Mini-Quiz
                                           perpendicular to a plane, then                                                                        Vocabulary Crossword
                                           every plane containing the line
                                           is perpendicular to the given
                                                                                                                                           Video: Determining Colinear Points
                                           plane                                                                                                Video: Defining a Plane
                                  G.G.8 Know and apply that if a plane
                                                                                                                                                 Discovery Education
                                         intersects two parallel planes,                                                                        Points, Lines, and Planes
                                         then the intersection is two
        parallel lines                   
G.G.9   Know and apply that if two                 Teacher Resource
        planes are perpendicular to the       Lesson: Defining Key Terms
        same line, they are parallel
                                          Lesson: Theorems Relating Lines and
                                          Multiple Choice: Practice with Lines
                                                      and Planes
           Chapter 10: 3D         G.G.10 Know and apply that the lateral
                                          edges of a prism are congruent
                                                                                 1. Students will classify 3-D
                                                                                    figures according to their
                                                                                                                           Cone                               Holt Text
 3/9-    Shapes (Volume and               and parallel.                             properties.                            Cylinder            10-1: pg 654-660 (Examples 1-4)
 3/18       Surface Area)                                                                                                  Net                 10-2: pg 661-668 (OPTIONAL)
                                  G.G.12    Know and apply that the volume       2. Students will learn and apply the
                                            of a prism is the product of the        formula for the surface area of a      Prism               10-3: pg 670-677 (OPTIONAL)
8 days   1. How can one                     area of the base and the altitude       prism and cylinder.
                                                                                                                           Right prism (in     10-4: pg 680-687 (Examples 1a, 2-5)
            generalize how to     G.G.13    Apply the properties of a regular    3. Students will learn and apply the       all of its forms)   10-5: pg 689-696 (Examples 1a, 2-5)
            find the volume of
                                            pyramid, including:
                                             Lateral edges are congruent
                                                                                    formula for the surface area of a
                                                                                    pyramid and a cone.
                                                                                                                           Pyramid             10-6: pg 697-704 (Examples 1a,b, 3b,4,5)
            any prism?                      Lateral faces are congruent                                                   Sphere              10-7: pg 705-712 (Examples 1-5)
                                             isosceles triangles                 4. Students will learn and apply the
                                                                                                                           Surface area        10-8: pg 714-721 (Examples 1-4)
                                            Volume of a pyramid equals             formula for the volume of a
                                             one-third the product of the           prism and cylinder.                    Volume
         2. How is the volume                area of the base and the altitude
                                                                                                                           Lateral edge              Vocab Graphing Organizers
                                                                                 5. Students will learn and apply the
            of a prism similar                                                                                                                  10-1: Know it Notes
                                  G.G.14    Apply the properties of a               formula for the volume of a            Lateral face
            to the volume                                                           pyramid and a cone.                                         10-4: Know it Notes
                                            cylinder, including:
                                                                                                                           Lateral surface
            formula of a                     Bases are congruent                                                                                10-5: Know it Notes
            cylinder?                       Volume equals the product of        6. Students will learn and apply the      Altitude
                                                                                                                                                10-6: Know it Notes
                                                                                    formula for the volume and
                                             the area of the base and altitude
                                             Lateral area of a right circular       surface area of a sphere.              Regular             10-7: Know it Notes
                                             cylinder equals the product of                                                Vertex              10-8: Know it Notes
         3. If you needed to
                                             an altitude and the
                                             circumference of the base
                                                                                                                           Slant height
            explain the process                                                                                            Radius                     Geometry Labs from Holt
            of finding surface
                                  G.G.15    Apply the properties of a right
                                            circular cone, including:
                                                                                                                           Great circle        10-1 Exploration
            area of any figure,             Lateral area equals one-half the                                                                   10-4 Exploration
                                             product of the slant height and
            how would you?                   the circumference of its base                                                                      10-4 Spreadsheet Lab
                                            Volume is one-third the product                                                                    10-4 Cylinder Lab Recording Sheet
                                             of the area of its base and its
                                             altitude                                                                                           10-5 Exploration
                                                                                                                                                10-5 Geometry Lab
                                  G.G. 16   Apply the properties of a
                                            sphere, including:
                                                                                                                                                10-6 Exploration
                                           The intersection of a plane and                                                                     10-7 Exploration
                                            a spere is a circle                                                                                 10-8 Exploration
                                           A great circle is the largest
                                            circle that can be drawn on a                                                                       10-8 Spreadsheet Lab Recording Sheet
                                           Two planes equidistant from
                                            the center of the sphere and                                                                                        JMAP
                                            intersecting the sphere do so in                                                                    G.G.12, G.G.13, G.G.14, G.G.15, G.G.16
    congruent circles
   Surface area is   4r 2     
                4 3           Lesson: Prisms
   Volume is     r          Lesson: Cylinders
                3             Lesson: Pyramids
                              Lesson: Cones
                              Lesson: Spheres
                              Practice: Working With Solids
                              Practice: Applied Questions Regarding
                                    G.G.49 Investigate, justify and apply         1.   identify tangents, secants and
                                                                                                                            interior of a circle                    Holt Text
 3/21-         Chapter 11                   theorems regarding chords of a             chords that intersect circles and    exterior of a circle    11-1: pg 746-750 (Examples 1-4)
 4/15           Circles                     circle: perpendicular bisectors or
                                            chords; the relative lengths of
                                                                                       use properties to solve
                                                                                                                            chord                       (GSP models or construction on pg
                                            chords as compared to their                                                     secant                       748 would allow students to discover
20 days        What are the                 distance from the center of the
                                                                                  2.   use properties of arcs and
                                                                                       chords of circles to solve
                                                                                                                            tangent of a circle          theorems 11-1-1, 11-1-2 and 11-1-3)
          properties of lines and                                                      problems                             point of tangency       11-2: pg 756-759 (Examples 1-4)
           angles that intersect    G.G.50 Investigate, justify and apply
                                                                                                                            congruent circles       11-4 pg. 772-775 (Examples1-4)
                                            theorems about tangent lines to a     3.   investigate and understand
          circles and how do we             circle: a perpendicular to the             theorems regarding inscribed         concentric circles      11-4 pg NY780A Extension (Example
             use them to solve              tangent at the point of tangency;          angles and central angles in a
                                                                                                                            tangent circles              1only , Note: This is a theorem they
                                            two tangents to a circle from the          circle
                problems?                   same external point; common                                                     common tangent               should be able to apply to solve
                                            tangents of two no-intersecting or    4.   find the measures of angles or                                     problems – pg 780C #2)
                                            tangent circles                            arcs formed by secants, chords       central angle
                                                                                                                                                     11-5 pg 782-785 (Examples 1-5)
                                                                                       and tangents that intersect a        arc
                                    G.G. 51 Investigate, justify and apply             circle                                                        11-6 pg 792-794 (Examples 1-4)
                                             theorems about the arcs                                                        minor arc               11-7 pg 799-801 (Examples1-3)
                                             determined by the rays of angles     5.   find the lengths of segments         major arc
                                             formed by two lines intersecting          formed by lines that intersect
                                             a circle when the vertex is:              circles                              semicircle                       GSP Labs from Holt
                                             inside the circle (two chords); on
                                             the circle (tangent and chord);      6.   write equations and graph
                                                                                                                            adjacent arcs           11-4 Exploration
                                             outside the circle (two tangents,         circles in the coordinate plane      congruent arcs          11-5 Exploration
                                             two secants, or tangent and
                                                                                                                            inscribed angle         11-5 Tech Lab p. 780
                                                                                                                            intercepted arc         11-6 Exploration
                                    G.G.52 Investigate, justify and apply
                                            theorems about arcs of a circle
                                                                                                                            subtend                 11-6 Tech Lab p. 790
                                            cut by two parallel lines                                                       secant segment                 Geometry Labs from Holt
                                    G.G. 53 Investigate, justify and apply
                                                                                                                            external secant         11-1 Exploration
                                            theorems regarding segments                                                      segment                 11-2 Tech Lab
                                            intersected by a circle: along two
                                            tangents from the same external
                                                                                                                            tangent segment         11-2 Exploration
                                            point; along two secants from the                                               radius                  11-5 Additional Geometry Lab
                                            same external point; along a
                                            tangent and a secant from the
                                                                                                                            diameter                11-6 Additional Geometry Lab
                                            same external point; along two                                                  center-radius form of   11-7 Exploration
                                            intersecting chords of a given
                                                                                                                             a circle
                                                                                                                                                           Vocab Graphic Organizers
                                    G.G.71 Write the equation of a circle,                                                                           11-1 know it notes 11-5 know it notes
                                           given its center and radius or
                                           given the endpoints of a diameter                                                                         11-2 know it notes 11-6 know it notes
G.G.72 Write the equation of a circle,
                                            11-4 know it notes 11-7 know it notes
       given its center and radius or
       given the endpoints of a                            JMAP
       diameter. Note: The center is an
       ordered pair of integers and the     G.G.49,G.G.50,G.G.51,G.G.52,G.G.53
       radius is an integer.                G.G.71,G.G.72,G.G.73,G.G.74
G.G.73 Find the center and radius of a
       circle, given the equation of the       
       circle in center-radius form
                                            Chords, Circles and Tangents
G.G.74 Graph circles of the form (x-h)2 +   Circles and Angles
       (y-k)2 = r2
                                            Circles Practice Regents Questions

                                            GSP: Angles and Circles
                                            GSP: Segments and Circles
                                            GSP: Tangents and Circles from scratch
              Chapter 12:            G.G.54 Define, investigate, justify, and
                                            apply isometries in the plane
                                                                                     1. Students will identify and draw
                                                                                        reflections, transformations,
                                                                                                                               Transformation                    Holt Text
 4/25-      Transformations                 (rotations, reflections, translations,      rotations, dilations and               Image              12-1: pg 824-830 (Examples 1,2,4)
  5/6                                       glide reflections)                          composition of transformations.
                                                                                                                               Preimage           12-2: pg 831-837 (Examples 1,3)
          1. How does a              G.G.55 Investigate, justify, and apply the      2. Students will apply theorems           Reflection in      12-3: pg 839-845 (Examples 1,3)
10 days      transformation                 properties that remain invariant            about isometries.                                          12-4: pg 848-853 (Example 1)
                                            under translations, rotations,
             affect the ordered             reflections, and glide reflections       3. Students will identify and             Point reflection   12-5: pg 856-862 (Example 1,2,3)
             pairs of the original
                                     G.G.56 Identify specific isometries by
                                                                                        describe symmetry in geometric
                                                                                                                               Translation        12-7: pg 872-879 (Examples 1 , 4)
             shape?                         observing orientation, numbers of                                                  Rotation           pg 906-907
                                            invariant points, and/or parallelism     4. Students will investigate
                                                                                                                               Isometry           pg 910-913
                                                                                        properties that are invariant
          2. How does a              G.G.57 Justify geometric relationships             under isometries and dilations.        Opposite
             change in ordered              (perpendicularity, parallelism,
                                                                                                                                isometry                     GSP from Holt Text
                                            congruence) using                        5. Students will use analytical
             pairs affect the               transformational techniques                 representations to justify claims      Direct isometry    12-1: Exploration
             position of a                                                                                                                         12-2: Exploration
                                            (translations, rotations, reflections)      about transformations.
                                                                                                                               Composition of
             geometric figure?                                                                                                                     12-4: Exploration
                                     G.G.58 Define, investigate, justify, and                                                   transformations
                                            apply similarities (dilations and
                                            the composition of dilations and                                                   Glide reflection
          3. How does a scale               isometries)                                                                        Symmetry
             factor affect a                                                                                                                        Vocabulary development – Graphing
             shape, its area and     G.G.59 Investigate, justify, and apply the                                                Line symmetry
             its position in the
                                            properties that remain invariant                                                   Rotational         12-1:know it notes
                                            under similarities
             coordinate plane?                                                                                                  symmetry           12-1:reading strategy
                                     G.G.60 Identify specific similarities by                                                  Enlargement        12-2:reading strategy
                                            observing orientation, numbers of
                                            invariant points, and/or parallelism                                               Reduction          12-3:know it notes
                                                                                                                               Invariant          12-5:know it notes
                                     G.G.61 Investigate, justify, and apply the
                                            analytical representations for                                                                         12-5:reading strategy
                                            translations, rotations about the
                                            origin of 90º and 180º, reflections
                                              over the lines   x  0, y  0 ,                                                                                      JMAP
                                              and   y  x , and dilations                                                                          G.G.54, G.G.55, G.G.56, G.G. 57,
                                              centered at the origin                                                                               G.G.58, G.G.59, G.G.60, G.G.61

                                                                                                                                                         Transformational Geometry
                                                                                                                                                   (Go to geometry section and find links
under transformational geometry)

TI 84 - transformations
TI 84 - rotations
GSP - transformations
GSP – transformations from scratch
Math in movies
                  Locus             G.G.22 Solve problems using compound
                                                                                    1.   Students will state and
                                                                                         illustrate the 5 fundamental
                                                                                                                                 Locus                            JMAP
 5/9-                                      loci                                          locus theorems                          Compound        G.G.22, G.G.23
 5/18     How can each of the 5     G.G.23 Graph and solve compound loci in
                                                                                                                                 Equidistant
                                           the coordinate plane                     2.   Student will solve problems
          fundamental loci be                                                            using compound loci                                         
8 days    applied to a real world                                                                                                                 Basic locus theorems
                                                                                    3.   Students will graph and solve
          context?                                                                       compound loci in the                                     Compound locus
                                                                                         coordinate plane
                                                                                                                                                            Other Resources
                                                                                                                                                       SEE ATTACHED PACKET
           Review Coordinate        G.G.69 Investigate, justify, and apply the
                                    properties of triangles and quadrilaterals in
                                                                                         1.    Students will use
                                                                                               coordinate geometry to
                                                                                                                                 Midpoint                      JMAP
 5/19-      Geometry Proofs         the coordinate plane, using the distance,                  justify and investigate           Distance        G.G.69
 5/31                               midpoint, and slope formulas                               properties of triangles
                                                                                                                                 Slope
          How can                                                                                                                Parallel         
8 days    mathematical                                                                                                           Perpendicular   Coordinate Geometry Proofs
          formulas be used to                                                                                                    Isosceles
          validate properties of                                                         2.    Students will
                                                                                                                                 Equilateral
                                                                                               investigate, justify and
          polygons?                                                                            apply properties of               Scalene                    Other Resources
                                                                                               quadrilaterals in the
                                                                                               coordinate plane                  Right
                                                                                                                                 Parallelogram        SEE ATTACHED PACKET
                                                                                                                                 Rectangle
                                                                                                                                 Rhombus
                                                                                                                                 Square
                                                                                                                                 Trapezoid

          FINAL EXAM                                                                                                                                
 6/1-     REVIEW                                                                                                                                  Geometry Review and Formula Sheet
 6/14                                                                                                                                             Theorems and Properties in Geometry
                                                                                                                                                  GeoCaching Activity
10 days                                                                                                                                           Geometry Jeopardy

Shared By:
Description: Properties of Triangle Centers Worksheets document sample