In the isosceles right triangles, each area equals half the square
of the side. Divide both sides of the pythagorean relationship
by 2 to prove the extension for this figure.

In
these triangles, each area equals one-fourth the square of the
side. Students should divide by 4 to prove the extension.

For equilateral triangles, multiply each term of the Pythagorean
theorem by

Solution

Multiply
by
and divide by 8 to prove the extension for semicircles.