1. 9.2
A diagonal of a square divides it into two congruent isosceles right triangles. Since the base angles of an isosceles triangle are congruent, the measure of each acute angle is 45°. So another name for an isosceles right triangle is a 45°-45°-90° triangle.
A 45°-45°-90° triangle is one type of special right triangle. You can use the Pythagorean Theorem to find a relationship among the side lengths of a 45°-45°-90° triangle.

2. 9.2

3. Example 1A: Finding Side Lengths in a 45°- 45º- 90º Triangle
9.2
Example 1A: Finding Side Lengths in a 45°- 45º- 90º Triangle
Find the value of x. Give your answer in simplest radical form.
By the Triangle Sum Theorem, the measure of the third angle in the triangle is 45°. So it is a 45°-45°-90° triangle with a leg length of 8.

4. Example 1B: Finding Side Lengths in a 45º- 45º- 90º Triangle
9.2
Example 1B: Finding Side Lengths in a 45º- 45º- 90º Triangle
Find the value of x. Give your answer in simplest radical form.
The triangle is an isosceles right triangle, which is a 45°-45°-90° triangle. The length of the hypotenuse is 5.
Rationalize the denominator.

5. 9.2
Check It Out! Example 1a
Find the value of x. Give your answer in simplest radical form.
By the Triangle Sum Theorem, the measure of the third angle in the triangle is 45°. So it is a 45°-45°-90° triangle with a leg length of
x = 20
Simplify.

6. 9.2
Check It Out! Example 1b
Find the value of x. Give your answer in simplest radical form.
The triangle is an isosceles right triangle, which is a 45°-45°-90° triangle. The length of the hypotenuse is 16.
Rationalize the denominator.

7. 9.2
Lesson Quiz: Part I
Find the values of the variables. Give your answers in simplest radical form.
x = 10; y = 20

8. 9.2
Lesson Quiz: Part II
Find the perimeter and area of each figure. Give your answers in simplest radical form.
5. a square with diagonal length 20 cm
6. an equilateral triangle with height 24 in.