Special Right Triangles

Objectives:• To use the properties of 45°-45°-90°

and 30°-60°-90° triangles.

Isosceles Right Triangle45°-45°-90° Triangle

a

a b c

1

2

3

4

5

l

Example

• In a 45°-45°-90° triangle, the hypotenuse is times as long as a leg. 2

45°

45°

x

x

2x

Example

• Find the hypotenuse.

13 ft

30°-60°-90° Trianglea b c

a =1

a = 2

a = 3

a = 4

a = 5

a= a

30°

60°a

b c

Example

• In a 30°-60°-90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is as long as the shorter leg. 3

30°

60°

x2x

3x

Example

• Find the remaining sides.

30°

60°

12

Equilateral Triangle

30°

60°

a

bc

(a is the shortest leg)