Understand similarity in terms of similarity transformations. (Geometry - Major Cluster) - Verify experimentally the properties of dilations given by a center and a scale factor:
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.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Understand similarity in terms of similarity transformations. (Geometry - Major Cluster) - 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.
Prove theorems involving similarity. (Geometry - Major Cluster) - 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.
Understand similarity in terms of similarity transformations. (Geometry - Major Cluster) - Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Define trigonometric ratios and solve problems involving right triangles. (Geometry - Major Cluster) - Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ★
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