# Chapter 7 4 Notes Special Right Triangles Goal

• Slides: 8

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 45 o-90 o triangle.

• 45 o-90 o Triangle Theorem: In a 45 o-90 o triangle, the hypotenuse is times as long as each leg. hypotenuse = ________ • Find the length of the hypotenuse. Ex. 1: Ex. 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 30 o-60 o-90 o triangle. • 30 o-60 o-90 o Triangle Theorem: In a 30 o-60 o-90 o 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 = ________

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: 60 o y 30 o x

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?

• Find the value of the variable. Ex. 10: Ex. 11: Ex. 12: 60 o b a 15