Definition
Pythagorean theorem
In a right triangle, the area of the square on the hypotenuse equals the areas of the squares on the two legs added together.
What it means
Find the right-angle corner first. The two sides that meet there are the legs; the side opposite is the hypotenuse. Imagine a square built on each side. The two leg-squares have exactly the same total area as the hypotenuse-square, which is why the side lengths are squared in the formula.
Remember it
Two leg-squares team up to equal the hypotenuse-square.
Example
A right triangle has legs 6 m and 8 m. If the hypotenuse is c, then c² = 6² + 8² = 36 + 64 = 100. Because c is a length, c is the positive square root of 100, so c = 10 m.
Watch for
The equation is guaranteed for right triangles, not for every triangle. The letter c must name the hypotenuse, the side opposite the right angle.
Common mix-up
Square the side lengths before adding. Adding the two leg lengths themselves is not the theorem.
Exact meaning
For a right triangle with leg lengths a and b and hypotenuse length c, the Pythagorean theorem states that a² + b² = c².