Section 7.3: The Pythagorean Theorem

Property

A triangle in which one of the angles is a right angle, or $90^\circ$, is called a right triangle. The side opposite the right angle is the longest side, called the hypotenuse. The other two sides are the legs.

If $c$ stands for the length of the hypotenuse, and the lengths of the two legs are $a$ and $b$, then:

In words: In a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.

Examples

• A right triangle has legs of length 3 cm and 4 cm. To find the hypotenuse $c$, we use $3^2 + 4^2 = c^2$. This gives $9 + 16 = 25$, so $c^2=25$, and the hypotenuse is 5 cm.

Property

In any right triangle $\triangle ABC$,

where $c$ is the length of the hypotenuse (the side opposite the right angle) and $a$ and $b$ are the lengths of the legs.