Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 13: Triangles 173

Hypotenuse

Leg

Leg

In a right triangle, the two sides that form the right

angle are called legs, and the side opposite the right

angle is called the hypotenuse.

The Pythagorean Theorem

One of the most famous theorems in mathematics can be applied to right triangles. It’s named

for Pythagoras, a sixth century B.C.E. Greek mathematician and philosopher. What Pythagoras

actually said about right triangles was probably something like “the square constructed on

the hypotenuse of a right triangle contains the squares on the other two sides.” His method of

investigating was actually drawing squares, but you can think about it from more of a number

point of view.

a

a

b

c

c

b

In any right triangle, if you measure

all the sides and square those

measurements, the square of the

length of the hypotenuse will be

equal to the sum of the squares of

the other two sides. If the legs of a

right triangle measure 5 inches and

12 inches, then the hypotenuse is

13 inches; 13^2 = 169 and 5^2 + 12^2 =

25 + 144 = 169.

The easiest way to remember the

Pythagorean theorem, and the most

common way, is in symbolic form.

If the legs of the right triangle are

labeled a and b and the hypotenuse

is c, then a^2 + b^2 = c^2.