PACING GUIDES FOR MATH
Grade Level: Tenth                       Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          14 Days                        14 Days                       22 Days                      10 Days

Unit Topic           Unit 1                         Unit 2                        Unit 3                       Unit 4
(Specify             Reasoning and Proof            Spatial Visual                Triangles                    2-Dimensional
that will be
Enduring             In proofs, deductive           Geometric figures and         The Pythagorean              Polygons are categorized
Understandings       reasoning about given          relationships can be          Theorem is essential to      by the number of sides.
(Give and/or         information is used to         represented in the            solving problems             Studying patterns can
demonstrate          reach mathematical             coordinate plane.             involving right triangles.   lead to geometric
necessary            conclusions.                    Geometric figures can        Congruent figures are        formulas and
information)          Theorems and properties       be measured in the            also similar figures, but    relationships.
                     exist that guarantee two       coordinate plane.             similar figures are not      Rectangles, squares, and
                     triangles are congruent or      The slope of a line is the   always congruent.            rhombi are
                     similar given certain          ratio of vertical change      Congruency and               parallelograms and
                     conditions.                    (rise) to horizontal          similarity have real life    belong to the set of
                      Relationships between         change (run).                 applications in art,         quadrilaterals.
                     lines, angles and figures      Slopes, distances and         architecture, and            Relationships exist
                     can be used to establish       midpoints can be              science.                     between sides, angles
                     additional mathematical        determined when a             Parallel and                 and segments in
                     relationships.                 segment is graphed in         perpendicular lines are      polygons.
                      Congruent figures are also    the coordinate plane.         used to prove triangles      By using the area
                     similar figures, but similar    A line’s direction and       congruent or similar.        formula of a rectangle,
                     figures are not always         steepness are                  30º-60º-90º and 45º-        we can derive area
                     congruent.                     determined by its slope.      45º-90º triangles are        formulas for other
                                                     Linear equations can be      similar triangles.           figures.
                                                    used to make
                                                 PACING GUIDES FOR MATH
Grade Level: Tenth                       Big Idea: Geometry             Prepared by Union County Schools

Time Frame:           14 Days                       14 Days                     22Days                      10 Days
Enduring              Parallel and perpendicular    A line’s slope and x- and   Special triangles have      Perimeter and
Understandings        lines are used to prove       y-intercepts have real      real world applications.    circumference are 1-
          con’t       triangles congruent or        world applications.          Relationships in special   dimensional measures,
                      similar.                                                  right triangles can be      while area is a 2-
                                                                                determined by the           dimenionsal measure.
                                                                                Pythagorean Theorem.         Measurement of
                                                                                                            geometric figures is an
                                                                                                            essential part everyday
Essential             Why write formal proofs?      Why is it important to      Why is the intersection     How can you use
Questions              Why are properties and       learn about geometric       point of special segments   patterns to find the sum
(Steps to check for   theorems about parallel       figures and relationships   in triangles important?     of the interior angles of
student               and perpendicular lines       in the coordinate plane?     What theorems              any polygon?
understanding)        useful in geometric proofs?    How do you determine       guarantee two triangles      How can you determine
                       How can reasoning about      information about a line    congruent?                  the measure of interior
                      geometric situations be       or segment graphed in        How do congruent           and exterior angles in
                      used to solve real life       the coordinate plane?       figures differ from         regular polygons?
                      problems?                      How does the Distance      similar figures?             How do you classify
                       If two figures are           Formula relate to the        Where are parallel and     quadrilaterals using
                      congruent or similar, what    Pythagorean Theorem?        perpendicular lines         special segments and
                      else do you know about        How do you represent        evident in everyday life?   properties?
                      their corresponding parts?    geometric figures in the     How are the angles          How do special
                      What theorems or              coordinate plane?           formed by parallel lines    segments in polygons
                      postulates (properties)        How do you measure         used to prove triangles     help solve everyday
                      guarantee two triangles       geometric figures using     congruent?                  situations?
                      congruent?                    the coordinate plane?
                                                 PACING GUIDES FOR MATH
Grade Level: Tenth                       Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          14 Days                        14 Days                      22 Days                    10 Days
Essential            How do congruent figures       How does slope describe      How are properties of      How can you derive the
Questions   con’t    differ from similar figures?   a line? How can you use      perpendicular lines used   various area formulas
                                                    an equation to make a        to prove congruent and     from the area of a
                                                    prediction?                  similar triangles?         rectangle?
                                                    What does the slope of        How is the Pythagorean    How can you find the
                                                    the line tell you?           Theorem related to the     areas of irregular
                                                     How do you write an         lengths of sides of        figures?
                                                    equation for a line?         special right triangles?    How does finding the
                                                    How do you write an          How does the concept of    area of the various
                                                    equation for a line if you   similarity apply to        figures apply to everyday
                                                    are given two points?        special right              situations?How are
                                                     How do you determine        triangles?How are right    perimeter,
                                                    the x- and y-intercepts      triangle relationships     circumference, and area
                                                    graphically and              used in the real world?    different from one
                                                    algebraically?                How do you find the       another?
                                                                                 lengths of sides of
                                                                                 special right triangles?

Standards            G-1.1 Demonstrate an           G-2.4 Use direct             G-3.1 Carry out a          G-2.3 Use the
                     understanding of the           measurement to               procedure to compute       congruence of line
                     axiomatic structure of         determine the length of a    the perimeter of a         segments and angles to
                     geometry                       segment, measure             triangle.                  solve problems.
                     using undefined terms,         of an angle, and distance    G-3.2 Carry out a          G-4.6 Apply congruence
                     definitions, postulates,       from a point to a line.      procedure to compute       and similarity between
                     theorems, and corollaries.     G-6.1 Use the distance       the area of a triangle.    shapes (including
                                                    formula to solve             G-3.3 Analyze how          quadrilaterals and
                                                    problems.                    changes in dimensions      polygons) to solve
                                                                                 affect the perimeter or    problems.
                                                                                 area of triangles.
                                                PACING GUIDES FOR MATH
Grade Level: Tenth                      Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          14 Days                       14 Days                       22 Days                     10 Days
Standards con’t      G-1.2 Communicate             G-6.2 Use the midpoint        G-3.4 Apply properties of   G-2.5 Carry out a
                     knowledge of geometric        formula to solve              isosceles and equilateral   procedure to create
                     relationships using           problems.                     triangles to solve          geometric constructions
                     mathematical                  G-2.2 Apply properties of     problems.                   (including
                     terminology appropriately.    parallel lines,               G-3.5 Use interior          midpoint of a line
                     G-1.7 Understand the          intersecting lines, and       angles, exterior angles,    segment, angle bisector,
                     historical development of     parallel lines cut            medians, angle bisectors,   perpendicular bisector of
                     geometry.                     by a transversal to solve     altitudes,                  a line segment, line
                     G-1.4 Formulate and test      problems.                     and perpendicular           through a given point
                     conjectures using a variety   G-2.5 Carry out a             bisectors to solve          that is parallel to a given
                     of tools such as concrete     procedure to create           problems.                   line,
                     models, graphing.             geometric constructions       G-3.6 Apply the Triangle    and line through a given
                     calculators, spreadsheets,    (including                    Sum Theorem to solve        point that is
                     and dynamic geometry          midpoint of a line            problems.                   perpendicular to a given
                     Software                      segment, angle bisector,      G-3.7 Apply the Triangle    line).
                     G-1.9 Demonstrate an          perpendicular bisector of     Inequality Theorem to       G-4.6 Apply congruence
                     understanding of how          a line segment, line          solve problems.             and similarity between
                     geometry applies to real      through a given point         G-3.8 Apply congruence      shapes (including
                     world contexts (including     that is parallel to a given   and similarity between      quadrilaterals and
                     architecture, construction,   line,                         triangles to solve          polygons) to solve
                     farming, astronomy).          and line through a given      problems.                   problems.
                                                   point that is                 G-3.9 Apply theorems to     G-2.6 Use scale factors
                                                   perpendicular to a given      prove triangles are         to solve problems
                                                   line).                        similar or congruent.       involving scale drawings
                                                                                 G-3.10 Use the              and
                                                                                 Pythagorean Theorem         models.
                                                                                 and its converse to solve
                                                PACING GUIDES FOR MATH
Grade Level: Tenth                      Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          14 Days                       14 Days           22 Days                     10 Days
Standards            G-1.10 Understand                               G-3.11 Use the              G-2.7 Use geometric
con’t                geometric relationships                         properties of 45-45-90      probability to solve
                     including constructions                         and 30-60-90 triangles      problems.
                     through investigations                          to solve problems.          G-4.1 Carry out a
                     using a variety of tools                        G-3.12 Use trigonometric    procedure to compute
                     such as straightedge,                           ratios (including sine,     the perimeter of
                     compass,                                        cosine, tangent) to solve   quadrilaterals,
                     paper folding, dynamic                          problems involving right    regular polygons, and
                     geometry software, and                          triangles.                  composite figures.
                     hand-held computing                                                         G-4.2 Carry out a
                     devices.                                                                    procedure to find the
                     G-1.3 Apply basic rules of                                                  area of quadrilaterals,
                     logic to determine the                                                      regular polygons, and
                     validity of the converse,                                                   composite figures.
                     inverse, and contrapositive                                                 G-4.3 Apply procedures
                     of a conditional statement                                                  to compute measures of
                     G-1.5 Use inductive                                                         interior and exterior
                     reasoning to formulate                                                      angles of polygons. area
                     conjectures.                                                                of quadrilaterals and
                     G-1.6 Use deductive                                                         regular polygons.
                     reasoning to validate                                                       G-4.4 Analyze how
                     conjectures with formal                                                     changes in dimensions
                     and informal proofs, and                                                    affect the perimeter or
                     give counterexamples to                                                     area of quadrilaterals
                     disprove a statement.                                                       and regular polygons
                                       PACING GUIDES FOR MATH
Grade Level: Tenth             Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          14 Days          14 Days               22 Days               10 Days
Standards                                                                         G-4.5 Apply
con’t                                                                             properties and
                                                                                  attributes of
                                                                                  quadrilaterals and
                                                                                  regular polygons
                                                                                  and their component
                                                                                  parts to solve
                                                                                  G-2.1 Infer missing
                                                                                  elements of visual or
                                                                                  numerical geometric
                                                                                  patterns (including
                                                                                  triangular numbers,
                                                                                  numbers, and
                                                                                  number of diagonals
                                                                                  in polygons).
                                                                                  G-2.7 Use geometric
                                                                                  probability to solve

(with other
discipline areas)

District                                                    Benchmark Exam
                                                 PACING GUIDES FOR MATH
Grade Level: Tenth                       Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          12 Days                             5 Days                           13 Days
Unit Topic           Unit 5                        Unit 6                     Unit 7
(Specify             3-Dimensional                 Transformations            Circles
that will be
Enduring             Three-dimensional             Transformations move or    Indirect measurement is
Understandings       figures have properties       map figures (preimages)    based on the properties
(Give and/or         similar to those of two-      onto their images.         of geometric figures.
demonstrate          dimensional figures.           Reflections, rotations,   Relationships exist
necessary                                          and translations are       among angles, segments,
information)                                       transformations that       lengths, circumference,
                                                   preserve shape and size    and area of circles.
                                                    Dilation is a
                                                   transformation that
                                                   preserves shape only

Essential            How are two-dimensional       Why do certain             How are the areas of
Questions            relationships connected       transformations preserve   polygons and circles
(Steps to check      to the properties of three-   shape and size while       related and applied?
for student          dimensional figures?          others only preserve       How are angles and
understanding)                                     shape?                     intercepted arcs of circles
                                                    How does combining        related and applied?
                                                   transformations affect
                                                   the final result?
                                                   How are the coordinates
                                                   affected by
                                                   transformations in the
                                                PACING GUIDES FOR MATH
Grade Level: Tenth                      Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          12 Days                            5 Days                             13 Days
Essential                                         coordinate plane?
Questions                                         How are scale factors
            con’t                                 used in transformations?

Standards            G-7.1 Carry out a            G-6.3 Apply                   G-5.1 Carry out a
                     procedure to compute         transformations               procedure to compute
                     the surface area of three-   (translation, reflection,     the circumference of
                     dimensional                  rotation, and dilation) to    circles.
                     objects (including cones,    figures in the coordinate     G-5.2 Carry out a
                     cylinders, pyramids,         plane using sketches and      procedure to compute
                     prisms, spheres, and         coordinates.                  the area of circles.
                     hemispheres).                G-6.4 Apply                   G-5.3 Analyze how a
                     G-7.2 Carry out a            transformations               change in radius affects
                     procedure to compute         (including translation        the circumference or area
                     the volume of three-         and dilation) to figures in   of a circle.
                     dimensional                  the coordinate plane          G-5.4 Carry out a
                     objects (including cones,    using matrices.               procedure to compute arc
                     cylinders, pyramids,         G-6.5 Carry out a             length or area of a sector
                     prisms, spheres,             procedure to represent        of a circle.
                     hemispheres, and             the sum of two vectors        G-5.5 Apply properties of
                     composite objects).          geometrically by using        component parts of a
                     G-7.3 Analyze how            the parallelogram             circle (including radii,
                     changes in dimensions        method.                       diameters, chords,
                     affect the volume of         G-6.6 Carry out a             sectors, arcs, and
                     objects (including           procedure to determine        segments) to solve
                     cylinders, prisms, and       the magnitude and             problems.
                     spheres).                    direction of the
                                                  resultant by direct
                                                  measurement using a
                                             PACING GUIDES FOR MATH
Grade Level: Tenth                   Big Idea: Geometry             Prepared by Union County Schools

Time Frame:          12 Days                       5 Days                      13 Days
Standards            G-7.4 Apply             scale drawing.         G-5.6 Apply
                     congruence and          G-6.7 Carry out a      properties of lines
                     similarity between      procedure to           that intersect
                     objects to solve        compute the            circles(including two
                     problems.               magnitude of the       secants, two
                     G-7.5 Apply a           resultant of two       tangents, or a secant
                     procedure to draw a     perpendicular          and a tangent) to
                     top-view, front-view,   vectors using the      solve problems.
                     and side-view of a      Pythagorean            G-5.7 Apply
                     three-dimensional       Theorem.               properties of central
                     object.                 G-6.8 Carry out a      angles, inscribed
                     G-7.6 Apply a           procedure to           angles, and arcs of
                     procedure to draw       determine the          circles to solve
                     an isometric view of    direction of the       problems.
                     a three-dimensional     resultant of two       G-2.7 Use geometric
                     object                  perpendicular          probability to solve
                                             vectors using direct   problems.

(with other
discipline areas)

District                                                            Final Exam

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