**Geometry 9.4 Special Right Triangles:**

**I) 45°: 45°:90° Triangle Theorem**: in a 45°, 45°, 90° triangle,

the hypotenuse is √2 times as long as each leg.

1x: 1x: x√2

**Example:**if the leg of a 45°: 45°: 90° triangle is 5, what is the other leg length and the hypotenuse length?

Since the legs are equal in length, the other leg is 5.

the hypotenuse would be 5√2

**II) 30 :60 : 90 triangle theorem:**in a 30º , 60º , 90º triangle,

the hypotenuse is 2 times as long as the shorter leg, and the longer leg is

√3 times as long as the shorter leg.

1x : x√3 : 2x

**Example**: if the shorter leg of a 30º , 60º , 90º triangle is 7, what is the length of the longer leg and the hypotenuse?

the longer leg is 7√3 and the hypotenuse is (2)(7) = 14