geometry software. Specify a sequence of transformations that will carry a given figure onto another. 4.4 Congruence and Transformations 4.6 Similarity and Transformations 5.3 Proving Triangle Congruence by SAS 5.5 Proving Triangle Congruence by SSS 5.6 Proving Triangle Congruence by ASA and AAS Understand congruence in terms of rigid motions Use rigid motion to map corresponding parts of congruent triangle onto each other. Explain triangle congruence in terms of rigid motions. Geometry - Congruence G.CO.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.CO.7 Use 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.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow the definition of congruence in terms of rigid motions. Reflect on Background Knowledge 4.1 Translations 4.2 Reflections 4.3 Rotations 4.4 Congruence and Transformations 5.2 Congruent Polygons 5.3 Proving Triangle Congruence by SAS 5.5 Proving Triangle Congruence by SSS 5.6 Proving Triangle Congruence by ASA and AAS Illustrative Mathematics Illuminations Teaching Channel Prove geometric theorems Prove theorems about lines and angles, triangles; and parallelograms. Geometry - Congruence G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, 2.5 2.6 3.2 Parallel Lines and Transversals 3.3 Proofs with Parallel Lines 3.4 Proofs with Perpendicular Lines 4.1 Translations Illustrative Mathematics Mars Task:
G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures Supporting clusters: G-MG 1-3: Modeling with Geometry: Apply geometric concepts in modeling situations 7.2 Properties of Parallelograms 7.3 Proving That a Quadrilateral is a Parallelogram 7.4 Properties of Special Parallelograms 7.5 Properties of Trapezoids and Kites 8.2 Proving Triangle Similarity by AA 8.3 Proving Triangle Similarity by SSS and SAS 9.3 Similar Right Triangles 11.1 Circumference and Arc Length 11.2 Areas of Circles and Sectors 11.5 Volumes of Prisms and Cylinders 11.6 Volumes of Pyramids 11.7 Surface Areas and Volumes of Cones 11.8 Surface Areas and Volumes of Spheres Modeling Task: Mars Task: Inside Mathematics High School Geometry – Unit 3 Express Geometric Properties with Equations; Extend Similarity to Circles Critical Area: Students investigate triangles and decide when they are similar; with this newfound knowledge and their prior understanding of proportional relationships, they define trigonometric ratios and solve problems using right triangles. They investigate circles and prove theorems about them. Connecting to their prior experience with the coordinate plane, they prove geometric theorems using coordinates and describe shapes with equations. Students extend their knowledge of area and volume formulas to those for circles, cylinders and other rounded shapes. They prove theorems, both with and without the use of coordinates. CLUSTERS COMMON CORE STATE STANDARDS Big Ideas Geometry Resources Use coordinates to simple geometric theorems algebraically Geometry - Expressing Geometric Properties with Equations G.GPE.4. Use coordinates to prove simple geometric theorems algebraically. For example, prove or 5.8 Coordinate Proofs 10.7 Circles in the Coordinate Plane Materials: Compass, straight-edge, graph paper, reflective surface,
Define trigonometric ratios and solve problems involving right triangles. Geometry - Similarity, Right Triangles, and Trigonometry G.SRT.6 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.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. G.SRT.8.1 Derive and use the trigonometric ratios for special right triangles (30°,60°,90°and 45°,45°,90°). CA 9.4 The Tangent Ratio 9.5 The Sine and Cosine Ratios 9.5 The Sine and Cosine Ratios 9.1 The Pythagorean Theorem 9.4 The Tangent Ratio 9.5 The Sine and Cosine Ratios 9.6 Solving Right Triangles Illustrative Mathematics Mars Task: Inside Mathematics: Explain volume formulas and use them to solve problems Visualize relationships between and three-dimensional objects. Geometric Measurement and Dimension G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. 11.1 Circumference and Arc Length 11.2 Areas of Circles and Sectors 11.3 Areas of Polygons 11.4 Three-Dimensional Figures 11.5 Volumes of Prisms and Cylinders (includes Cavalieri’s principle) 11.6 Volumes of Pyramids 11.8 Surface Areas and Volumes of Spheres Student Journal p.184 Section 6.5 Exploration Illustrative Mathematics Illuminations Mathematics Vision Project: