## SAT SUBJECT TEST MATH LEVEL 1

## PLANE GEOMETRY

## CHAPTER 9 Triangles

### SPECIAL RIGHT TRIANGLES

Let *x* be the length of each leg and let *h* be the length of the hypotenuse of an isosceles right triangle. By the Pythagorean theorem,

**Key Fact H7**

**In a 45-45-90 right triangle, the sides are x, x, and x**

**.**

• **If you are given the length of a leg, multiply it by** **to get the length of the hypotenuse.**

• **If you are given the length of the hypotenuse, divide it by** **to get the length of each leg.**

**EXAMPLE 5:** To find the area of a square whose diagonal is 8, note that the diagonal divides the square into two isosceles right triangles. So .

Let 2*x* be the length of each side of equilateral *PQR,* in which altitude has been drawn. Then *PQS* is a 30-60-90 right triangle, and its sides are *x*, 2*x*, and *h*. By the Pythagorean theorem,

**Key Fact H8**

**In a 30-60-90 right triangle, the sides are x, x**

**, and 2**

*x*.**If you know the length of the shorter leg (**

*x*):• **Multiply it by** **to get the length of the longer leg.**

• **Multiply it by 2 to get the length of the hypotenuse.**

**If you know the length of the longer leg ( a):**

• **Divide it by** **to get the length of the shorter leg.**

• **Multiply the length of the shorter leg by 2 to get the length of the hypotenuse.**

**If you know the length of the hypotenuse ( h):**

• **Divide it by 2 to get the length of the shorter leg.**

• **Multiply the length of the shorter leg by** **to get the length of the longer leg.**