The Pythagorean theorem states that in a right triangle, the squares of the two shorter sides add to the square of the hypotenuse. It only holds for right triangles, which is why identifying the right angle comes first.
Math Dictionary / Pythagorean Theorem
Pythagorean Theorem
The Pythagorean theorem says that in a right triangle, a^2 + b^2 = c^2.
GeometryGrade 8Algebra 1GEDSATACT
What it means
The legs are a and b. The hypotenuse, c, is the longest side across from the right angle.
Also called: a squared plus b squared
Examples
| 3^2 + 4^2 = 5^2 |
| 5, 12, 13 is a right-triangle triple |
| Use it to find distance on a coordinate plane |
Common mistake
The formula works for right triangles only.
Try one
Question: A right triangle has legs 6 and 8. What is the hypotenuse?
Show answer
6^2 + 8^2 = 36 + 64 = 100, so c = 10.