Geometry: Similarity, Right Triangles, and Trigonometry Archive

Verify experimentally the properties of dilations given by a center and a scale factor:

A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves…

The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar;…

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two…

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to…