High School Mathematics Domain: Geometry—Similarity, Right Triangles, and Trigonometry CCSS Grade-Level Standards DLM Essential Elements CLUSTER: Understand similarity in terms of similarity transformations. G-SRT.1. Verify experimentally the properties of dilations given by a center and a scale factor: G-SRT.1.a. A dilation takes a line not passing through the center of the dilation to a parallel Not applicable. line, and leaves a line passing through the center unchanged. See EE.G-CO.6–8. G-SRT.1.b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G-SRT.2. Given two figures, use the definition of similarity in terms of similarity Not applicable. 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 See EE.G-CO.6–8. proportionality of all corresponding pairs of sides. Not applicable. G-SRT.3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. See EE.G-CO.6–8. CLUSTER: Prove theorems involving similarity. G-SRT.4. Prove theorems about triangles. Theorems include: a line parallel to one side of a Not applicable. triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. Not applicable. G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. See EE.G-CO.6–8. CLUSTER: Define trigonometric ratios, and solve problems involving right triangles. G-SRT.6. Understand that by similarity, side ratios in right triangles are properties of the angles Not applicable. 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 Not applicable. angles. G-SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in Not applicable. applied problems. CLUSTER: Apply trigonometry to general triangles.
High School Mathematics Domain: Geometry—Similarity, Right Triangles, and Trigonometry CCSS Grade-Level Standards DLM Essential Elements CLUSTER: Understand similarity in terms of similarity transformations. G-SRT.1. Verify experimentally the properties of dilations given by a center and a scale factor: Not applicable. See EE.G-CO.6–8. G-SRT.1.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. G-SRT.1.b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G-SRT.2. 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. Not applicable. See EE.G-CO.6–8. G-SRT.3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Not applicable. See EE.G-CO.6–8. CLUSTER: Prove theorems involving similarity. 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. Not applicable. G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Not applicable. See EE.G-CO.6–8. CLUSTER: Define trigonometric ratios, and solve problems involving right triangles. 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. Not applicable. G-SRT.7. Explain and use the relationship between the sine and cosine of complementary angles. Not applicable. G-SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Not applicable. CLUSTER: Apply trigonometry to general triangles.
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