Students will learn how to find missing side lengths and angles in similar polygons. Finding missing angles is easy. Finding missing side lengths involves setting up and solving proportions. Special attention should be given to similar triangles. After doing some routine problems, give your students this challenge: Look at the triangle below. A perpendicular has been dropped from the apex to the base of the triangle, cutting the base into segments of \(64\) cm and \(36\) cm. What are the side lengths of the original triangle?

Here's the solution. Finally, give your students this challenge. The construction in the solution provided is quite tricky.