Similarity — Similarity of Triangles

About this lesson

This unit teaches the cases of similarity of triangles, focusing on the AA (angle-angle) similarity postulate, the SAS (side-angle-side) similarity theorem, and the SSS (side-side-side) similarity theorem. It also covers corollaries about a line drawn parallel to one side of a triangle creating a similar triangle, and about the altitude to the hypotenuse of a right triangle separating it into two similar triangles. The unit includes worked examples and exercises that involve proving triangles similar, finding unknown side lengths using proportions, and applying these concepts to geometric figures such as triangles and circles. A historical context is given with Thales measuring the height of a pyramid using shadows, and a group activity involves drawing triangles with given angles and comparing side ratios. By the end, a student should be able to identify similar triangles using the stated postulates and theorems, prove similarity, and calculate unknown lengths using proportional relationships.