My older son is reviewing geometry this summer using Art of Problem Solving’s Introduction to Geometry book. He’s been choosing pretty challenging problems for our movies, too. Today’s was a “star” problem in chapter 4. I thought his work was a nice illustration of what a kid learning about similar triangles can look like.

Here’s the introduction to the problem, some progress, and getting stuck:

Here’s the search for the second set of similar triangles. We end with a ration that will help us solve the problem, but we don’t go all the way to the end.