What is the Pythagorean Theorem?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides: a² + b² = c².

Understanding the Parts

c = Hypotenuse (longest side, opposite right angle)

a and b = Legs (the two shorter sides)

Example Problem

Find the hypotenuse of a right triangle with legs of 3 and 4.

c² = 3² + 4² = 9 + 16 = 25

c = √25 = 5

Finding a Leg

If c = 13 and a = 5, find b:

b² = c² - a² = 169 - 25 = 144

b = √144 = 12