1. Objectives Justify and apply properties of 45°-45°-90° triangles.

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 ___________ 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.

4. Example 1A: Finding Side Lengths in a 45°- 45º- 90º Triangle
Find the value of x. Give your answer in simplest radical form.

5. Example 1B: Finding Side Lengths in a 45º- 45º- 90º Triangle
Find the value of x. Give your answer in simplest radical form.

6. Example 1C
Find the value of x. Give your answer in simplest radical form.

7. A 30°-60°-90° triangle is another special right triangle
A 30°-60°-90° triangle is another special right triangle. You can use an equilateral triangle to find a relationship between its side lengths.

8. Example 2A: Finding Side Lengths in a 30º-60º-90º Triangle
Find the values of x and y. Give your answers in simplest radical form.
22 = 2x
Hypotenuse = 2(shorter leg)
11 = x
Divide both sides by 2.
Substitute 11 for x.

9. Example 2B: Finding Side Lengths in a 30º-60º-90º Triangle
Find the values of x and y. Give your answers in simplest radical form.
Rationalize the denominator.
y = 2x
Hypotenuse = 2(shorter leg).
Simplify.

10. Example 2C
Find the values of x and y. Give your answers in simplest radical form.
y = 2(5)
y = 10
Simplify.

11. Check It Out! Example 2D
Find the values of x and y. Give your answers in simplest radical form.

12. Example 4: Using the 30º-60º-90º Triangle Theorem
An ornamental pin is in the shape of an equilateral triangle. The length of each side is 6 centimeters. Josh will attach the fastener to the back along AB. Will the fastener fit if it is 4 centimeters long?