Given a triangle with sides of lengths a, b, and c. Let the semiperimeter be defined by

Prove:

s(s - c) = (s - a)(s - b)IF AND ONLY IF the triangle is a Right Triangle with right angle at C and hypotenuse of length c.

Proof:

Therefore, the triangle is a right triangle with legs a and b and hypothenuse c. Conversely, if we begin with a given right triangle, the steps can be reversed and lead to the conclusion that the equation holds.