Chapter 7.4 Notes: Special Right Triangles

Goal: You will use the relationships among the sides in special right triangles.

• Part I:

• Draw an isosceles right triangle.

• What do you know about the two legs?

• What do you know about the measures of the acute angles of an isosceles right triangle?

• Another name for an isosceles right triangle is a

45o-45o-90o triangle.

• 45o-45o-90o Triangle Theorem:

In a 45o-45o-90o triangle, the hypotenuse is

times as long as each leg.

hypotenuse = ________________

• Find the length of the hypotenuse.

Ex.1: Ex.2:

2

• Find the lengths of the legs in the triangle. Ex.3: Ex.4: 2

Part II:• Draw an equilateral triangle with side length of 6 cm

• What do you know about an equilateral triangle?1. ________________________________2. ________________________________

• When you divide an equilateral triangle in half, the two triangles formed are called a 30o-60o-90o triangle.

• 30o-60o-90o Triangle Theorem:

In a 30o-60o-90o triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is

times as long as the shorter leg.

hypotenuse = _______________

longer leg = ________________

3

Ex.5: Find the values of x and y. Write your answer in simplest radical form.

• Find the value of the variable.

Ex.6: Ex.7:

60o

y

30o x

3

Ex.8: The shorter leg of a 30-60-90 triangle has a length of . What are the lengths of the other two sides?

Ex.9: A baseball diamond is a square. The distance from base to base is 90 feet. How far does the second baseman throw a ball to home plate?

6

• Find the value of the variable.

Ex.10: Ex.11:

Ex.12:

60o

b

a

15