The triangle T has sides of length a, b and c and angles ?, ? and 90 ^o . Two enlargements are made of triangle T. The triangle T _a , is an enlargement by scale factor a and the triangle T _b is an enlargement by scale factor b. The triangles T _a and T _b are fitted together as shown in the diagram. Prove that the resulting triangle is an enlargement of triangle T by the scale factor c and use this fact to prove Pythagoras Theorem.

You can use the interactivity below to explore this problem. Make three enlargements of yellow triangles and fit the enlargements, which may need to be rotated, into the grey outline.