Education Technology

Overlapping Squares

Activity Overview

This activity is designed as a teacher demonstration tool to introduce students to the notion of ‘proof’ as it applies to geometry. Initially the diagram looks complicated, however, add a couple of lines and it’s obvious! Then students have to go beyond what is obvious in an illustration to mathematical proof.


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!


  • 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.