Figure 1 and figure 2 above are congruent squares. Both figures have been split into smaller shapes consisting of squares and right triangles. All of the triangles are congruent, and they have leg lengths of a and b, with hypotenuse c, as marked in figure 1.

Question

has an area of c2 square units.

In figure 2,
is a2 square units, while
is b2 square units.

Given that
, it can be concluded that c2 = a2 + b2.

Answer 1

This is known as the Pythagorean Theorem, where in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore, in this case, c2 = a2 + b2.