1. Chapter 7.4 Notes: Special Right Triangles
Goal: You will use the relationships among the sides in special right triangles.

2. 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.

3. 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:

4. 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. ________________________________

5. 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 = ________________

6. Find the value of the variable. Ex.6: Ex.7:
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

7. Ex. 8: The shorter leg of a 30-60-90 triangle has a length of
Ex.8: The shorter leg of a 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?

8. Find the value of the variable. Ex.10: Ex.11:15