Lesson 7-3: The Pythagorean Theorem

Property

In a right triangle, the legs (sides $a$ and $b$) are the two sides that form the right angle. The hypotenuse (side $c$) is the side opposite the right angle and is always the longest side.

Examples

• In a right triangle like $\Delta RST$ (where $\angle S = 90^\circ$), the legs are $\overline{RS}$ and $\overline{ST}$ because they form the 90° angle. The hypotenuse is $\overline{RT}$ because it is the longest side across from the 90° angle.
• A right triangle has side lengths of 8 cm, 15 cm, and 17 cm. The longest side is 17 cm, so it is the hypotenuse. The other two sides, 8 cm and 15 cm, are the legs.
• In a triangle where the sides adjacent to the right angle measure $x$ and $y$, and the third side is $z$, the sides $x$ and $y$ are the legs. The side $z$ is the hypotenuse.

Explanation

Property

A right triangle contains a 90° angle. The side opposite the right angle is the hypotenuse ($c$), and the other two sides are the legs ($a$ and $b$).

The Pythagorean Theorem states that for any right triangle: