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

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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 -45 o -90 o triangle

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Theorem 7.8 45 o -45 o -90 o Triangle Theorem:

In a 45 o -45 o -90 o triangle, the hypotenuse is 2 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

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Theorem 7.9 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 3 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 3 30 o x

Ex.8: The shorter leg of a 30-60-90 triangle has a 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: a 60 o 15 b