Objectives
Introduce students to the notion of proof. The initial problem seems complicated, it’s not. Add a couple of well chose lines and the problem no longer looks difficult, but students must go beyond intuiting and produce a proof!
Vocabulary
- Proof
- Similar Triangles
- Conditions for Similarity
About the Lesson
Two squares are placed such that centre of one is the vertex of another. The larger square is rotated creating over overlapping section (polygon). What is the area of this polygon? The results are quite surprising. Now prove it. Again, the results are surprising.