# Geometry Unit 02 - Coordinate Geometry

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```					                                                      Geometry Unit 2 – Coordinate Geometry

Unit Length______8 days________                                                                              Unit Dates ___Aug. 29 – Sep. 9_______

Quality Core Standards                                                        Common Core Standards
G.CO.1. Know precise definitions of angle, circle, perpendicular line,
B.1.d. Use the language of mathematics to communicate increasingly              parallel line, and line segment, based on the undefined notions of point,
complex contexts (e.g. expressions, formulas, tables, charts, graphs,           line, distance along a line, and distance around a circular arc.
relations, functions) and understand relationships.                             G-CO.3. Given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself.
B.1.f. Make mathematical connections among concepts, across disciplines,        G-CO.4. Develop definitions of rotations, reflections, and translations in
and everyday experiences.                                                       terms of angles, circles, perpendicular lines, parallel lines, and line
segments.
C.1.a Use definitions, basic postulates, and theorems about points, lines,      G-SRT.1. Verify experimentally the properties of dilations given by a center
angles, and planes to write proofs and to solve problems.                       and a scale factor:
A dilation takes a line not passing through the center of the dilation to a
C.1.b Use inductive reasoning to make conjectures and deductive                 parallel line, and leaves a line passing through the center unchanged.
reasoning to arrive at valid conclusions.                                       The dilation of a line segment is longer or shorter in the ratio given by the
scale factor.
D.1.a Identify and model plane figures, including collinear and non-collinear   G-SRT.7. Explain and use the relationship between the sine and cosine of
points, lines, segments, rays, and angles using appropriate mathematical        complementary angles.
symbols.                                                                        G-GPE.2. Derive the equation of a parabola given a focus and directrix.
G-CO.6. Use geometric descriptions of rigid motions to transform figures
D.1.b Identify vertical, adjacent, complementary, and supplementary angle       and to predict the effect of a given rigid motion on a given figure; given two
pairs and use them to solve problems (e.g. solve equations, use in proofs).     figures, use the definition of congruence in terms of rigid motions to decide
if they are congruent.
G-CO.7. Use the definition of congruence in terms of rigid motions to show
that two triangles are congruent if and only if corresponding pairs of sides
and corresponding pairs of angles are congruent.
G-GMD.4. Identify the shapes of two-dimensional cross-sections of three-
dimensional objects, and identify three-dimensional objects generated by
rotations of two-dimensional objects. G-CO.8. Explain how the criteria for
triangle congruence (ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
G-CO.9. Prove theorems about lines and angles. Theorems include:
vertical angles are congruent; when a transversal crosses parallel lines,
alternate interior angles are congruent and corresponding angles are
congruent; points on a perpendicular bisector of a line segment are exactly
those equidistant from the segment’s endpoints.
G-CO.10. Prove theorems about triangles. Theorems include: measures of

FCPS 2011-12
Geometry Unit 2 – Coordinate Geometry
Quality Core Standards                                                  Common Core Standards
interior angles of a triangle sum to 180°; base angles of isosceles triangles
are congruent; the segment joining midpoints of two sides of a triangle is
parallel to the third side and half the length; the medians of a triangle meet
at a point.
G-CO.11. Prove theorems about parallelograms. Theorems include:
opposite sides are congruent, opposite angles are congruent, the
diagonals of a parallelogram bisect each other, and conversely, rectangles
are parallelograms with congruent diagonals.
G-SRT.4. Prove theorems about triangles. Theorems include: a line
parallel to one side of a triangle divides the other two proportionally, and
conversely; the Pythagorean Theorem proved using triangle similarity.
G-SRT.10. (+) Prove the Laws of Sines and Cosines and use them to solve
problems.
G-C.1. Prove that all circles are similar.
G-C.5. Derive using similarity the fact that the length of the arc intercepted
by an angle is proportional to the radius, and define the radian measure of
the angle as the constant of proportionality; derive the formula for the area
of a sector.

G-MG.3. Apply geometric methods to solve design problems (e.g.,
designing an object or structure to satisfy physical constraints or minimize
cost; working with typographic grid systems based on ratios).

Summative Assessment                            Formative Assessment                Critical Vocabulary             Prior Vocabulary
KCCT-like                                        On-going assessments                     Midpoint Formula                Slope
Constructed Response Questions AND               Entrance/exit slips                      Distance Formula
Multiple Choice Questions/Multiple Choice        Journals                                 Parallel lines
Question Sets                                    quizzes                                  Perpendicular lines
ACT-like                                                                                  Isosceles triangle
Equilateral triangle
Scalene triangle
Rectangle
Parallelogram
Rhombus
Square
Trapezoid
Isosceles trapezoid

FCPS 2011-12
Geometry Unit 2 – Coordinate Geometry
Glencoe Textbook Correlation
Chapter 1.7
Chapter 3.8
Chapter 6.7 -6.8

Unit 2 Coordinate Geometry

Less      Learning Target/I                Teacher Facilitated                   Student Engagement                       Formative/Summative             Materials/Resou
on #      Can Statement:                   Learning Strategies:                  Strategies (including                    Assessment:                     rces Needed:
Communication, Thinking
and/or Technology):
1       I can use the distance           Use graph on marker boards to         Distance and midpoint formulas,          Practice 1.7                    Markers, marker boards
8/29     formula and the midpoint         practice with distance and midpoint   practicing on marker boards, straight                                    graph paper copies
formula to find distances,       formulas (We are pondering            forward problems, finding distances                                      workbooks
midpoints and missing            battleship)                           and midpoints
information.
8/30     I can use the distance           Demonstration of using the same       Distance and midpoint formulas,          Pages 54-55/select problems     Copies of pages 54-55
formula and the midpoint         formula to find different missing     finding the missing endpoint given the
formula to find distances,       information, missing endpoints or     midpoint and finding a missing
midpoints and missing            coordinates                           coordinate given the distance.
information.
2       I can use the slope formula to   Review types of slope, review         Pair and share with problems             Pair and share worksheet with   Worksheet- Pair and
8/31     determine whether sets of        algebra one process of finding        stating two pairs of coordinates.        coordinates of lines            Share
points determine lines that      slope, and comparing two slopes to    Each student finds one slope and
are parallel or perpendicular    determine the relationships of your   then compares with other student to
(or neither).
lines.                                complete, stating the relationship
between the two lines as parallel,
perpendicular or neither. ( using
marker boards if desired)

FCPS 2011-12
Geometry Unit 2 – Coordinate Geometry
3      I can write linear equations    Review Algebra I process of using            Understand that as long as the point is on the   Algebra 2 Practice 2.4/21-24,28.a
9/1     that are parallel or                                                         line, it can be used in the point slope form!                                        Worksheets
point slope formula to write the
perpendicular to a given line                                                All of your equations can be different
equation of a line. BTW- don’t               looking and still represent the same line!
through a given point.          simplify!
4      I can use the distance,         Review properties of specific types of       Fill in graphic organizers with specific         Practice 6.7                        Workbooks
9/2     midpoint and slope formulas     triangles and Quadrilaterals. Have           clues as to how you would proceed in                                                 Graphic organizers
to determine relationships on   students fill in shapes in graphic           justifying that the given figure is what
the coordinate plane.           organizers of Isosceles, scalene, and        you know it to be!
equilateral as well as the Quadrilaterals
5      I can use coordinate            Graphs to name arbitrary points for          Fill in graph paper with missing                 Practice 6.8                        Workbooks
9/6     geometry to locate algebraic    geometric shapes such as right               coordinates, keep in notes (Mason)                                                   Graph Paper
points for figures based on     triangles, squares, rectangles etc. Direct
their geometric properties.     instruction on using properties of the
shapes to find points
9/7     See all above                   Jeopardy ! Categories: Parallel or           Play jeopardy on teams chosen by                 Unit 2 Review sheets                Review sheets
Perpendicular, Midpoint Formula,             teacher, review sheets for homework
Distance Formula, Triangles,
9/8     See all above                   Go over review sheets, have students         Put review problems on board, make               Unit 2 review sheets,               Review Sheets
work problems on board , answer final        sure they are correct so you can
questions before tomorrow’s test.            STUDY!
9/9     See all above                   Test Unit 2                                  Test Unit 2                                      Test Unit 2                         Tests, Scantrons

FOR WHOLE UNIT:

Modifications/Adaptation (as noted in IEP, 504 Plans, ILP’s and/or ESL Plans):

Differentiation: (content, process and/or product according to readiness and/or interest, GSSP)

Re-teaching Processes and/or Strategies:
FCPS 2011-12
Geometry Unit 2 – Coordinate Geometry
Pre-assessment and Summative Assessment Attached:

FCPS 2011-12
Geometry Unit 2 – Coordinate Geometry

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