G-SRT. Similarity, Right Triangles, and Trigonometry
G-SRT.A. Understand similarity in terms of similarity transformations
G-SRT.A.1. Verify experimentally the properties of dilations given by a center and a scale factor:
G-SRT.A.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.A.1.b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G-SRT.A.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.
G-SRT.A.3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
- Bank Shot
- Congruence of parallelograms
- Extensions, Bisections and Dissections in a Rectangle
- Finding triangle coordinates
- Folding a square into thirds
- How far is the horizon?
- Is this a rectangle?
- Points from Directions
- Slope Criterion for Perpendicular Lines
- Tangent Line to Two Circles
- Unit Squares and Triangles
G-SRT.B. Prove theorems involving similarity
G-SRT.B.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.B.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
G-SRT.C. Define trigonometric ratios and solve problems involving right triangles
G-SRT.C.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.C.7. Explain and use the relationship between the sine and cosine of complementary angles.
G-SRT.C.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
- No tasks yet illustrate this standard.
- No tasks yet illustrate this standard.
- No tasks yet illustrate this standard.