Pythagorean Theorem - Proof Without Words

Finding a Square

Looking at the three angles on the left side of the left square, we have

Even though angles 1 and 2 are in different triangles within the left square, they are congruent to the acute angles of a single right triangle. Therefore, angles 1 and 2 are complementary and their measures sum to 90 degrees.

Substituting in the three-angle expression, we have

This means angle 3 is a right angle, as is each corner of the bold figure. Therefore, it must be a square whose area is given by cē.