Definition: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a<sup>2</sup> + b<sup>2</sup> = c<sup>2</sup>.
What does it say?
For a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. The hypotenuse is the side opposite the right angle, and it is always the longest side.
How do you find the hypotenuse?
A ramp rises 5 feet over a horizontal run of 12 feet. Then c2 = 25 + 144 = 169, so c = 13 feet.
How do you find a leg?
Subtract. If the hypotenuse is 17 and one leg is 8, then b2 = 289 – 64 = 225, so b = 15.
Does the converse work?
Yes. If a triangle has sides 7, 24, and 25, check 49 + 576 = 625 = 252. It is a right triangle.
What are the Pythagorean triples?
Whole-number sets such as 3-4-5, 5-12-13, 8-15-17, and multiples like 6-8-10.
What is a common mistake?
Adding the sides before squaring. Square first, then add. Also, do not use the theorem for triangles without a right angle.
Where to learn it
- The Pythagorean Theorem and Its Converse – lesson
- Finding Distance Between Points on a Grid – lesson