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BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Content Standard # and Identifier (AHSGEReview) Content Standard Description **AHSGE – REVIEW (if needed) Modeling With Geometry 39 [G-MG1] 39. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [G-MG1] Congruence 1 [G-CO1] 1.Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [G-CO1] Page 1 of 28 1st 9 Weeks AHSGE ACT/Quality Core Standards Description VII-6 II-1 II-4 II-3 VII-2 Standards for Quality Core Mathematical Prerequisites Practice Skill Algebra 2 D.1.a E.1.h IV-2 VII-1 C.1.a Textbook Resources Glencoe - Geometry 0-3 Simple Probability 0-4 Algebraic Expressions 0-5 Linear Equations 0-6 Linear Inequalities 0-8 Systems of Linear Equations 0-9 Simplifying Radicals 1-1 Extend Lab (Describing What You See) 6 1-1 1-2 1-3 1-4 1-5 Points, Lines, Planes Linear Measure Distance and Midpoint Angle Measure Angle Relationships BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Congruence Content Content Standard Description Standard # and Identifier 12 12. Make formal geometric [G-CO12] constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. [G-CO12] 1st 9 Weeks AHSGE ACT/Quality Core Standards Description IV-2 D.1.a VII-1 D.1.c D.1.d Standards for Quality Core Mathematical Prerequisites Practice Skill 5 6 Textbook Resources Glencoe - Geometry 1-2 Linear Measure 1-3 Distance and Midpoint 1-4 Angle Measure 1-5 Extend Lab Constructing Perpendiculars 1-6 Extend Lab 2-D Figures Expressing Geometric Properties with Equations 32 [G-GPE6] 32. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. [G-GPE6] IV-2 G.1.c 2 7 8 Algebra 2 1-3 Distance and Midpoint Expressing Geometric Properties with Equations 33 [G-GPE7] IV-1,2 F.2.a G.1.c 1-6 Two-Dimensional Figures 36 [GGMD3] IV-1,2 D.4.a F.2.a F.2.c 1 2 5 6 1 2 3 4 5 Algebra 2 Geometric Measurement and Dimension 33.) Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* [G-GPE7] 36.) Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [GGMD3] Page 2 of 28 1-7 Three – Dimensional Figures BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Modeling with Geometry Content Content Standard Description Standard # and Identifier 39 39.) Use geometric shapes, their [G-MG1] measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [G-MG1] Prep Modeling with Geometry Congruence 41 [G-MG3] 9 [G-CO9] Congruence 12 [G-CO12] Page 3 of 28 1st 9 Weeks AHSGE ACT/Quality Core Standards Description D.1.a E.1.h Standards for Quality Core Mathematical Prerequisites Practice Skill 4 5 7 **These lessons are not on the course of study. They are to prep for the objectives that will be covered in lessons 2.5 -2.8 9. Prove theorems about lines and angles. [G-CO9] 12. Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. [G-CO12] 1-7 Extend 2-D Representations of 3-D Objects Algebra 2 PreCalculus 41. Apply geometric methods to solve design [G-MG3] VII-1 C.1.a C.1.b C.1.e D.1.b D.1.c D.1.a D.1.c D.1.d 1 4 5 2 3 5 5 6 Textbook Resources Glencoe - Geometry 2-1 – 2-4, 2-6 (Prep for 2-5 – 2.8) 2-5 Postulates and Paragraph Proofs Algebra 2 PreCalculus 2-7 Proving Segment Relationships 2-8 Proving Angle Relationships 2-7 Proving Segment Relationships BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Content Standard # and Identifier Congruence 1 [G-CO1] Congruence 9 [G-CO9] Congruence 12 [G-CO12] Expressing Geometric Properties with Equations Modeling with Geometry Page 4 of 28 31 [G-GPE5] 41 [G-MG3] Content Standard Description 1.) Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [G-CO1] 9.) Prove theorems about lines and angles. [G-CO9] 1st 9 Weeks AHSGE ACT/Quality Core Standards Description VII-1 C.1.a VII-1 12.) Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. [G-CO12] IV-2 31.) Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5] IV-2 41.) Apply geometric methods to solve design [G-MG3] IV-2 Standards for Quality Core Mathematical Prerequisites Practice Skill 6 Textbook Resources Glencoe - Geometry 3-1 Parallel Line and Transversals 3-2 Angles and Parallel Lines C.1.a C.1.b C.1.e D.1.b D.1.c D.1.a D.1.c D.1.d 2 3 5 Algebra 2 PreCalculus C.1.d D.1.f G.1.a G.1.c 3 8 Algebra 2 PreCalculus 3-3 Explore (Investigating Slope) 3-3 Slopes of Lines 3-4 Extend (Equations of Perpendicular Bisectors) 3-4 Equations of Lines 1 4 5 Algebra 2 PreCalculus 3-6 Perpendiculars and Distance 5 6 3-2 Angles and Parallel Lines 3-5 Proving Lines Parallel 3-2 Explore (Angles and Parallel Lines) 3-5 Proving Lines Parallel 3-6 Perpendiculars and Distance BCSS Mathematics Pacing Guide 2013 - 2014 Geometry 2nd 9 Weeks AHSGE ACT/Quality Core Standards Description VII-4 D.1.a D.1.c D.1.d Domain Content Standard # and Identifier Content Standard Description Congruence 12 [G-CO12] 12.) Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. [G-CO12] Congruence 10 [G-CO10] 10.) Prove theorems about triangles. [G-CO10] VII-4 C.1.e D.2.b D.2.j 2 3 5 Congruence 7 [G-CO7] 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-CO7] VII-4 C.1.g E.1.b 3 Page 5 of 28 Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources 4-1 Classifying Triangles 4-2 Explore Angles of Triangles 4-4 Extend Proving Constructions 4-4 Proving Triangles Congruent (SSS/SAS) 4-5 Proving Triangles Congruent (ASA/AAS) 4-6 Isosceles and Equilateral Triangles 5 6 Algebra 2 PreCalculus 4-2 Angles of Triangles 4-3 Congruent Triangles 4-4 Proving Triangles Congruent (SSS/SAS) 4-5 Proving Triangles Congruent (ASA/AAS) 4-6 Isosceles and Equilateral Triangles 4-8 Triangles and Coordinate Proof 4-3 Congruent Triangles 4-7 Explore Congruence Transformations 4-7 Congruence Transformations BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Content Standard # and Identifier Content Standard Description Similarity, Right Triangles, and Trigonometry 18 [G-SRT5] 18.) Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [G-SRT5] Congruence 5 [G-CO5] Congruence 6 [G-CO6] Page 6 of 28 2nd 9 Weeks AHSGE ACT/Quality Core Standards Description Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources D.2.d E.1.e E.1.g 3 4 6 7 Algebra 2 PreCalculus 5.) Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [GCO5] E.1.a E.1.e 3 5 7 4-3 Congruent Triangles 4-4 Extend Proving Constructions 4-4 Proving Triangles Congruent (SSS/SAS) 4-5 Extend Congruence in Right Triangles 4-5 Proving Triangles Congruent 4-7 Explore Congruence Transformations 6.) Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. [GCO6] E.1.a 3 5 7 VII-4 4-7 Explore Congruence Transformations 4-7 Congruence Transformations BCSS Mathematics Pacing Guide 2013 - 2014 Geometry 2nd 9 Weeks AHSGE ACT/Quality Core Standards Description Domain Content Standard # and Identifier Content Standard Description Congruence 2 [G-CO2] 2.) Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). [G-CO2] G.1.e 5 6 4-7 Congruence Transformations Congruence 8 [G-CO8] 8.) Explain how the criteria for triangle congruence, angle-side-angle (ASA), side-angle-side (SAS), and side-sideside (SSS), follow from the definition of congruence in terms of rigid motions. [G-CO8] C.1.f 2 3 4-7 Congruence Transformations Expressing Geometric Properties with Equations 30 [G-GPE4] 30.) Use coordinates to prove simple geometric theorems algebraically. [GGPE4] G.1.b G.1.c 2 3 7 Algebra 2 Congruence 9 . [G-CO9] 9.) Prove theorems about lines and angles. [G-CO9] C.1.a C.1.b C.1.e D.1.b D.1.c 2 3 5 Algebra 2 PreCalculus Page 7 of 28 Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources 4-8 Triangles and Coordinate Proof 5-1Bisectors of Triangles BCSS Mathematics Pacing Guide 2013 - 2014 Geometry 2nd 9 Weeks AHSGE ACT/Quality Core Standards Description Domain Content Standard # and Identifier Content Standard Description Congruence 10 . [G-CO10] 10.) Prove theorems about triangles. [G-CO10] Congruence 12 [G-CO12] 12.) Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. [G-CO12] Modeling with Geometry 41 [G-MG3] 41.) Apply geometric methods to solve design [G-MG3] VII-4 Modeling with Geometry 39 [G-MG1] 39.) Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [G-MG1] VII-3 Page 8 of 28 VII-4 Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources C.1.e D.2.b D.2.j 2 3 5 Algebra 2 PreCalculus 5-1 Bisectors of Triangles 5-2 Medians and Altitudes 5-3 Inequalities in One Triangle 5-4 Indirect Proof 5-5Triangle Inequality 5-6 Inequalities in Two Triangles D.1.a D.1.c D.1.d 5 6 5-1 Explore Constructing Bisectors 5-2 Explore Constructing Medians and Altitudes 5-5 Explore Triangle Inequality 1 4 5 5-1 Bisectors of Triangles 5-2 Medians and Altitudes of Triangles 5-5 Triangle Inequality 4 5 7 6-1 Angles of Polygons D.1.a E.1.h BCSS Mathematics Pacing Guide 2013 - 2014 Geometry 2nd 9 Weeks AHSGE ACT/Quality Core Standards Description Domain Content Standard # and Identifier Content Standard Description Congruence 11 [G-CO11] VII-3 Congruence 12 . [G-CO12] Expressing Geometric Properties with Equations 30 [G-GPE4] 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-CO11] 12.) Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. [G-CO12] 30.) Use coordinates to prove simple geometric theorems algebraically. [GGPE4] Modeling with Geometry 41 [G-MG3] 41.) 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).* [G-MG3] VII-3 Page 9 of 28 Standards for Mathematical Practice Quality Core Prerequisites Skill C.1.e C.1.i D.2.j 2 3 5 Algebra 2 PreCalculus VII-3 D.1.a D.1.c D.1.d 5 6 VII-3 G.1.b 2 3 7 G.1.c 1 4 5 Textbook Resources 6-2 Parallelograms 6-3 Tests for Parallelograms 6-4 Rectangles 6-5 Rhombi and Squares 6-3 Explore Parallelograms 6-3 Tests for Parallelograms 6-4 Rectangles 6-5 Rhombi and Squares Algebra 2 6-2 Parallelograms 6-3 Tests for Parallelograms 6-4 Rectangles 6-5 Rhombi and Squares 6-6 Trapezoids and Kites 6-6 Trapezoids and Kites BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Content Standard # and Identifier Content Standard Description Modeling with Geometry 41 41.) 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).* [G-MG3] 15.) Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. [G-SRT2] Similarity, Right Triangles, and Trigonometry Congruence [G-MG3] 15 [G-SRT2] 2 [G-CO2] Congruence 10 [G-CO10] Page 10 of 28 2.) Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). [G-CO2] 10.) Prove theorems about triangles.. [G-CO10] 3rd 9 Weeks AHSGE ACT/Quality Core Standards Description Quality Core Prerequisites Skill Textbook Resources 1 4 5 7-1 Ratios and Proportions 7-7 Scale Drawings and Models C.1.h 3 5 7 7-2 Similar Polygons 7-3 Similar Triangles 7-6 Similarity Transformations G.1.e 5 6 7-6 Similarity Transformations C.1.e D.2.b D.2.j 2 3 5 VII-7 VII-3 Standards for Mathematical Practice Algebra 2 PreCalculus 7-4 Parallel Lines and Proportional Parts BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Content Standard # and Identifier Content Standard Description Congruence 12 12.) Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software.. [G-CO12] 16.) Use the properties of similarity transformations to establish the angleangle (AA) criterion for two triangles to be similar. [G-SRT3] [G-CO12] Similarity, Right Triangles, and Trigonometry Similarity, Right Triangles, and Trigonometry Similarity, Right Triangles, and Trigonometry Page 11 of 28 16 G-SRT3] 17 [G-SRT4] 18 [G-SRT5] 3rd 9 Weeks AHSGE ACT/Quality Core Standards Description D.1.a D.1.c D.1.d Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources 5 6 7-4 Parallel Lines and Proportional Parts VII-3 C.1.h 3 7-3 Similar Triangles 7-6 Similarity Transformations 17.) Prove theorems about triangles.. [G-SRT4] VII-3 D.2.e 3 5 7-3 Similar Triangles 7-4 Parallel Lines and Proportional Parts 7-5 Parts of Similar Triangles 18.) Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [G-SRT5] VII-3 D.2.d E.1.e E.1.g 3 4 6 7 7-3 Similar Triangles 7-4 Parallel Lines and Proportional Parts 7-5 Parts of Similar Triangles 7-6 Similarity Transformations BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Content Standard # and Identifier Content Standard Description Expressing Geometric Properties with Equations 31 31.) Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5] 32.) Find the point on a directed line segment between two given points that partitions the segment in a given ratio. [G-GPE6] Expressing Geometric Properties with Equations Modeling with Geometry Congruence [G-GPE5] 32 [G-GPE6] 41 [G-MG3] 10 [G-CO10] Similarity, Right Triangles, and Trigonometry Page 12 of 28 17 [G-SRT4] 41.) 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).* [G-MG3] 10.) Prove theorems about triangles.. [G-CO10] 17.) Prove theorems about triangles. [G-SRT4] 3rd 9 Weeks AHSGE ACT/Quality Core Standards Description Standards for Mathematical Practice Quality Core Prerequisites Skill C.1.d D.1.f G.1.a G.1.c 3 8 Algebra 2 7-3 Extend Proofs of Perpendicular and Parallel Lines G.1.e 2 7 8 Algebra 2 7-4 Parallel Lines and Proportional Parts 1 4 5 VII-2 C.1.e D.2.b D.2.j D.2.e Textbook Resources 8-2 Pythagorean Theorem and Converse 2 3 5 Algebra 2 PreCalculus 8-2 Explore Proofs Without Words 3 5 Algebra 2 PreCalculus 8-1 Geometric Mean BCSS Mathematics Pacing Guide 2013 - 2014 Geometry 3rd 9 Weeks AHSGE ACT/Quality Core Standards Description Domain Content Standard # and Identifier Content Standard Description Similarity, Right Triangles, and Trigonometry Similarity, Right Triangles, and Trigonometry 18 18.) Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [G-SRT5] D.2.d E.1.e E.1.g 3 4 6 7 8-1 Geometric Mean 19.) Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle leading to definitions of trigonometric ratios for acute angles. [G-SRT6] H.1.b 2 6 7 8 8-3 Special Right Triangles 8-4 Explore Trigonometry 8-4 Extend Secant, Cosecant, Cotangent 8-4 Trigonometry 20.) Explain and use the relationship between the sine and cosine of complementary angles. [G-SRT7] H.1.b 2 3 Algebra 2 8-4 Trigonometry D.2.e H.1.a H.1.b H.1.c 1 4 5 Algebra 2 8-2 Pythagorean Theorem and Converse 8-4 Trigonometry 8-5 Angles of Elevation and Depression 8-6 Law of Sines and Law of Cosines Similarity, Right Triangles, and Trigonometry Similarity, Right Triangles, and Trigonometry Page 13 of 28 [G-SRT5] 19 [G-SRT6] 20 [G-SRT7] 21 [G-SRT8] 21.) Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [GSRT8] VII-2 Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Content Standard # and Identifier Content Standard Description Similarity, Right Triangles, and Trigonometry Similarity, Right Triangles, and Trigonometry Expressing Geometric Properties with Equations Congruence 22 22.) (+) Prove the Law of Sines and the Law of Cosines and use them to solve problems. [G-SRT10] [G-SRT10] 23 [G-SRT11] 32 [G-GPE6] 2 [G-CO2] Page 14 of 28 3rd 9 Weeks AHSGE ACT/Quality Core Standards Description Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources D.2.f 1 4 Algebra 2 PreCalculus 8-6 Law of Sines and Law of Cosines 23.) (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). [G-SRT11] D.2.f 1 4 Algebra 2 PreCalculus 8-6 Extend Ambiguous Case 8-6 Law of Sines and Law of Cosines 32.) Find the point on a directed line segment between two given points that partitions the segment in a given ratio. [G-GPE6] G.1.c 2 7 8 Algebra 2 2.) Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). [G-CO2] G.1.e 5 6 8-7 Vectors 9-1 Reflections 9-2 Translations 9-3 Explore Rotations 9-3 Rotations 9-4 Explore Compositions of Transformations 9-4 Compositions of Transformations 9-6 Dilations BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Content Standard # and Identifier Content Standard Description Congruence 3 3.) Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. [G-CO3] 4.) Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. [GCO4] [G-CO3] Congruence 4 [G-CO4] Congruence 5 [G-CO5] Page 15 of 28 5.) Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [G-CO5] 3rd 9 Weeks AHSGE ACT/Quality Core Standards Description Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources 3 5 7 9-5 Symmetry C.1.a E.1.e 5 6 7 9-1 Reflections 9-2 Translations 9-3 Rotations 9-4 Explore Compositions of Transformations 9-4 Compositions of Transformations E.1.a E.1.e 3 5 7 9-1 Reflections 9-2 Translations 9-3 Explore Rotations 9-3 Rotations 9-4 Explore Compositions of Transformations 9-4 Compositions of Transformations BCSS Mathematics Pacing Guide 2013 - 2014 Geometry 3rd 9 Weeks AHSGE ACT/Quality Core Standards Description Domain Content Standard # and Identifier Content Standard Description Congruence 6 6.) Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. [G-CO6] E.1.a 3 5 7 9-1 Reflections 9-2 Translations 9-3 Rotations 9-4 Compositions of Transformations 9-6 Explore Dilations 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-CO7] C.1.g E.1.b 3 9-1 Reflections 9-2 Translations 9-3 Rotations 9-4 Compositions of Transformations 9-6 Extend Establishing Triangle Congruence and Similarity 8.) Explain how the criteria for triangle congruence, angle-side-angle (ASA), side-angle-side (SAS), and side-sideside (SSS), follow from the definition of congruence in terms of rigid motions. [G-CO8] C.1.f 2 3 9-6 Extend Establishing Triangle Congruence and Similarity [G-CO6] Congruence 7 [G-CO7] Congruence 8 [G-CO8] Page 16 of 28 Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Content Standard # and Identifier Content Standard Description Congruence 12 12.) Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. [G-CO12] [G-CO12] Similarity, Right Triangles, and Trigonometry Similarity, Right Triangles, and Trigonometry Page 17 of 28 14a [G-SRT1a] 14b . [G-SRT1b] 14.) Verify experimentally the properties of dilations given by a center and a scale factor. [G-SRT1] a. A dilation takes a line not passing through the center of the dilation to a parallel line and leaves a line passing through the center unchanged. [GSRT1a] 14.) Verify experimentally the properties of dilations given by a center and a scale factor. [G-SRT1] b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. [G-SRT1b] 3rd 9 Weeks AHSGE ACT/Quality Core Standards Description D.1.a D.1.c D.1.d Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources 5 6 9-1 Reflections 9-3 Explore Rotations 9-5 Extend Exploring Constructions with a Reflective Device 2 5 6 8 9-6 Explore Dilations 9-6 Dilations 2 5 6 8 9-6 Explore Dilations 9-6 Dilations BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Content Standard # and Identifier Content Standard Description Similarity, Right Triangles, and Trigonometry 15 15.) Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. [G-SRT2] 16.) Use the properties of similarity transformations to establish the angleangle (AA) criterion for two triangles to be similar. [G-SRT3] Similarity, Right Triangles, and Trigonometry Page 18 of 28 . [G-SRT2] 16 [G-SRT3] 3rd 9 Weeks AHSGE ACT/Quality Core Standards Description Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources C.1.h E.1.c E.1.d 3 5 7 9-6 Extend Establishing Triangle Congruence and Similarity C.1.h 3 9-6 Extend Establishing Triangle Congruence and Similarity BCSS Mathematics Pacing Guide 2013 - 2014 Geometry 4th 9 Weeks AHSGE ACT/Quality Core Standards Description Domain Content Standard # and Identifier Content Standard Description Congruence 1 [G-CO1] 1.) Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [G-CO1] Congruence 12 [G-CO12] 12.) Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software.. [G-CO12] Congruence 13 [G-CO13] 13.) Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. [G-CO13] Circles 24 [G-C1] 24.) Prove that all circles are similar. [G-C1] Page 19 of 28 IV-1 IV-1 Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources C.1.a 6 10-1 Circles and Circumference D.1.a D.1.c D.1.d 5 6 10-3 Arcs and Chords 10-5 Extend Inscribed and Circumscribed Circles 10-5 Tangents 5 6 10-5 Extend Inscribed and Circumscribed Circles 3 5 Algebra 2 PreCalculus 10-1 Circles and Circumference BCSS Mathematics Pacing Guide 2013 - 2014 Geometry 4th 9 Weeks AHSGE ACT/Quality Core Standards Description Domain Content Standard # and Identifier Content Standard Description Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources Circles 25 [G-C2] 25.) Identify and describe relationships among inscribed angles, radii, and chords [G-C2] D.3.a D.3.b D.3.c 1 3 5 PreCalculus 10-1Circles and Circumference 10-2 Measuring Angles and Arcs 10-3 Arcs and Chords 10-4 Inscribed Angles 10-5 Tangents Circles 26 [G-C3] 26.) Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. [G-C3] D.2.b D.3.d 3 5 10-4 Inscribed Angles 10-5 Extend Inscribed and Circumscribed Circles Circles 27 [G-C4] 27.) (+) Construct a tangent line from a point outside a given circle to the circle. [G-C4] D.3.c 1 2 10-5 Tangents Circles 28 [G-C5] F.1.d F.1.e 2 3 6 7 10-2 Measuring Angles and Arcs Expressing Geometric Properties with Equations 29 [G-GPE1] 28.) 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-C5] 29.) Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. [G-GPE1] G.1.d D.1.e 2 3 7 8 10-8 Equations of Circles Page 20 of 28 IV-1 BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Content Standard # and Identifier Content Standard Description Expressing Geometric Properties with Equations Expressing Geometric Properties with Equations Geometric Measurement and Dimension 30 [G-GPE4] 30.) Use coordinates to prove simple geometric theorems algebraically. [G-GPE4] 32 [G-GPE6] 32.) Find the point on a directed line segment between two given points that partitions the segment in a given ratio. [G-GPE6] 35 [G-GMD1] 35.) Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone.. [G-GMD1] Modeling with Geometry 41 [G-MG3] 41.) 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).* [G-MG3] Expressing Geometric Properties with Equations 33 [G-GPE7] 33.) Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* [G-GPE7] Page 21 of 28 4th 9 Weeks AHSGE ACT/Quality Core Standards Description IV-1 IV-1 Standards for Mathematical Practice Quality Core Prerequisites Skill G.1.b G.1.c 2 3 7 Algebra 2 10-8 Equations of Circles G.1.c 2 7 8 Algebra 2 10-8 Equations of Circles D.4.a F.2.a F.2.b E.1.f E.1.h 3 4 5 10-1 Circles and Circumference 1 4 5 10-3 Arcs and Chords 1 2 5 6 11-1 Areas of Parallelograms and Triangles F.2.a G.1.c Textbook Resources BCSS Mathematics Pacing Guide 2013 - 2014 Geometry 4th 9 Weeks AHSGE ACT/Quality Core Standards Description Domain Content Standard # and Identifier Content Standard Description Modeling with Geometry 40 [G-MG2] Modeling with Geometry 41 [G-MG3] Circles 28 [G-C5] 40.) Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot).* [G-MG2] 41.) 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).* [G-MG3] 28.) 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-C5] Geometric Measurement and Dimension 35 [G-GMD1] Page 22 of 28 35.) Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. [G-GMD1] IV-1 Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources 1 4 5 11-2 Extend Population Density 1 4 5 11-2 Areas of Trapezoids, Rhombi, Kites 11-3 Areas of Circles and Sectors IV-1 F.1.d F.1.e 2 3 6 7 IV-1 D.4.a F.2.a F.2.b E.1.f E.1.h 3 4 5 Algebra 2 PreCalculus 11-3 Areas of Circles and Sectors BCSS Mathematics Pacing Guide 2013 - 2014 Geometry 4th 9 Weeks AHSGE ACT/Quality Core Standards Description Domain Content Standard # and Identifier Content Standard Description Expressing Geometric Properties with Equations 34 (Alabama) 34.) Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. (Alabama) Modeling with Geometry 41 [G-MG3] Modeling with Geometry 39 [G-MG1] Geometric Measurement and Dimension 35 [G-GMD1] 41.) 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).* [G-MG3] 39.) Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [G-MG1] 35.) Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. [G-GMD1] Page 23 of 28 G.1.c IV-1 Standards for Mathematical Practice Quality Core Prerequisites Skill 11-4 Explore Investigating Areas of Regular Polygons 11-4 Extend Regular Polygons on the Coordinate Plane 11-4 Areas of Regular Polygons and Composite Figures 11-4 Areas of Regular Polygons and Composite Figures 1 6 1 4 5 IV-1, VII-3 D.1.a E.1.h 4 5 7 IV-1 D.4.a F.2.a F.2.b E.1.f E.1.h 3 4 5 Textbook Resources 11-5 Areas of Similar Figures Algebra 2 PreCalculus 12-4 Volumes of Prisms and Cylinders 12-5 Volume of Pyramids and Cones 12-6 Surface Areas and Volumes of Spheres BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Content Standard # and Identifier Geometric Measurement and Dimension 36 [G-GMD3] 36.) Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [G-GMD3] Geometric Measurement and Dimension Geometric Measurement and Dimension 37 (Alabama) 38 [G-GMD4] Modeling with Geometry 39 [G-MG1] Page 24 of 28 Content Standard Description 4th 9 Weeks AHSGE ACT/Quality Core Standards Description IV-1 Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources D.4.a F.2.a F.2.c 1 2 3 4 5 12-4 Volumes of Prisms and Cylinders 12-5 Volumes of Pyramids and Cones 12-6 Surface Area and Volumes of Spheres 37.) Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama) D.4.a F.2.a F.2.c 1 6 12-8 Congruent and Similar Solids 38.) 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-GMD4] 39.) Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [G-MG1] D.4.b 4 5 7 12-1 Representations of 3-D Figures D.1.a E.1.h 4 5 7 12-3 Surface Areas of Pyramids and Cones BCSS Mathematics Pacing Guide 2013 - 2014 Geometry 4th 9 Weeks AHSGE ACT/Quality Core Standards Description Domain Content Standard # and Identifier Content Standard Description Modeling with Geometry 40 [G-MG2] 40.) Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot).* [G-MG2] 1 4 5 12-4 Volumes of Prisms and Cylinders 12-5 Volumes of Pyramids and Cones Modeling with Geometry 41 [G-MG3] 41.) 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).* [G-MG3] 1 4 5 12-2 Surface Areas of Prisms and Cylinders Modeling with Geometry 41 [G-MG3] 1 4 5 13-4 Simulations Using Probability to Make Decisions 42 [S-MD6] 41.) 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).* [G-MG3] 42.) (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] 1 4 5 13-4 Simulations Page 25 of 28 F.1.c Standards for Mathematical Practice Quality Core Prerequisites Skill Textbook Resources BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Domain Content Standard # and Identifier Content Standard Description Using Probability to Make Decisions 43 [S-MD7] 43.) (+) Analyze decisions and strategies using probability concepts (e.g. product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7] Page 26 of 28 4th 9 Weeks AHSGE ACT/Quality Core Standards Description VII-6 F.1.c Standards for Mathematical Practice 1 2 4 Quality Core Prerequisites Skill Textbook Resources 13-3 Geometric Probability 13-5 Probabilities of Independent and Dependent Events BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Essential Vocabulary st nd 1 9 Weeks 2 9 Weeks Chapter 1 acute angle, adjacent angles, angle, angle bisector, area, base, between, circumference, collinear, complementary angles, concave, cone, congruent, construction, convex, coplanar, cylinder, degree, distance, edge, equiangular polygon, equilateral polygon, exterior, face, interior, intersection, line, line segment, linear pair, midpoint, n-gon, obtuse angle, opposite rays, perimeter, perpendicular, plane, Platonic solid, point, polygon, polyhedron, prism, pyramid, ray, regular polygon, regular polyhedron, right angle, segment bisector, side, space, sphere, supplementary angles, surface area, undefined term, vertex, vertex of a polygon, vertical angles, volume Chapter 4 acute triangle, auxiliary line, base angles, congruence transformation, congruent polygons, coordinate proof, corollary, corresponding parts, equiangular triangular, equilateral triangle, exterior angle, flow proof, included angle, included side, isosceles triangle, obtuse triangle, reflection, remote interior angles, right triangle, rotation, scalene triangle, rotation, scalene triangle, translation, vertex angle Chapter 2 algebraic proof, axiom, compound statement, conclusion, conditional statement, conjecture, contra-positive, converse, counterexample, deductive argument, deductive reasoning, disjunction, formal proof, hypothesis, ifthen statement, inductive reasoning, informal proof, inverse, logically equivalent, negation, paragraph proof, postulate, proof, related conditionals, statement, theorem, truth table, truth value, two-column proof Chapter 6 base, base angle, diagonal, isosceles trapezoid, kite, legs, midsegment of a trapezoid, parallelogram, rectangle, rhombus, square, trapezoid Page 27 of 28 Chapter 5 altitude, centroid, circumcenter, concurrent lines, incenter, indirect proof, indirect reasoning, median, orthocenter, perpendicular bisector, point of concurrency, proof by contradiction 3rd 9 Weeks Chapter 7 cross products, dilation, enlargement, extremes, means, midsegment of a triangle, proportion, ratio, reduction, scale, scale drawing, scale factor, scale model, similar polygons, similarity transformation Chapter 8 angle of depression, angle of elevation, component form, cosine, direction, geometric mean, inverse cosine, inverse sine, inverse tangent, Law of Cosines, Law of Sines, magnitude, Pythagorean triple, resultant, sine, standard position, tangent, trigonometric ratio, trigonometry, vector Chapter 9 angle of rotation, axis symmetry, center of rotation, composition of transformations, glide reflection, line of reflection, line of symmetry, line symmetry, magnitude of symmetry, order of symmetry, plane symmetry, rotational symmetry, symmetry, translation vector 4th 9 Weeks Chapter 10 adjacent arcs, arc, arc length, center, central angle, chord, chord segment, circle, circumference, circumscribed, common tangent, compound locus concentric circles, congruent arcs, diameter, external secant segment, inscribed, inscribed angle, intercepted arc, major arc, minor arc, pi, point of tangency, radius, secant, secant segment, semicircle, tangent Chapter 11 apothem, base of a parallelogram, base of a triangle, center of a regular polygon, central angle of a regular polygon, composite figure, height of a parallelogram, height of a trapezoid, height of a triangle, radius of a regular polygon, sector of a circle Chapter 12 altitude, axis, base edges, composite solid, congruent solid, cross section, Euclidean geometry, great circle, isometric view, lateral area, lateral edge, lateral face, non-Euclidean geometry, oblique cone, oblique solid, regular pyramid, right cone, right solid, similar solids, slant height, spherical geometry, topographic map Chapter 13 circular permutation, combination, complement, compound events, conditional probability, dependent events, expected value, factorial, Fundamental Counting Principle, geometric probability, independent events, mutually exclusive events, permutation, probability model, probability tree, random variable, sample space, simulation, tree diagram BCSS Mathematics Pacing Guide 2013 - 2014 Geometry Essential Vocabulary st 1 9 Weeks Chapter 3 alternate exterior angles, alternate interior angles, consecutive interior angles, corresponding angles, equidistant, parallel lines, parallel planes, point-slope form, rate of change, skew lines, slope, slope-intercept form, transversal Page 28 of 28 nd 2 9 Weeks 3rd 9 Weeks 4th 9 Weeks