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Tuesday, February 2 Essential Questions How do I use the relationships among the sides in special right triangles?

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**Special Right Triangles**

5.1 Special Right Triangles Theorem 5.1: 45o – 45o – 90o Triangle Theorem In a 45o – 45o – 90o triangle, the hypotenuse is ____ times as long as each leg.

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**Special Right Triangles**

5.1 Special Right Triangles Example 1 Find lengths in a 45o – 45o – 90o triangle Find the value of x. Solution By the Triangle Sum Theorem, the measure of the third angle must be ______. Then the triangle is a ____-____- 90o triangle, so by Theorem 5.1, the hypotenuse is ___ times as long as each leg. ____-____- 90o Triangle Theorem Substitute.

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**Special Right Triangles**

5.1 Special Right Triangles Example 1 Find lengths in a 45o – 45o – 90o triangle Find the value of x. Solution You know that each of the two congruent angles in the triangle has a measure of ____ because the sum of the angle measure in a triangle is 180o. ____-____- 90o Triangle Theorem Substitute. Divide each side by ___. Simplify.

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**Special Right Triangles**

5.1 Special Right Triangles Checkpoint. Find the value of x.

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**Special Right Triangles**

5.1 Special Right Triangles Checkpoint. Find the value of x.

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**Special Right Triangles**

5.1 Special Right Triangles Theorem 5.2: 30o – 60o – 90o Triangle Theorem In a 30o – 60o – 90o triangle, the hypotenuse is ____ as long as the shorter leg, and the longer leg is ____ times as long as the shorter leg.

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**Special Right Triangles**

5.1 Special Right Triangles Example 2 Find the height of an equilateral triangle Music You make a guitar pick that resembles an equilateral triangle with side lengths of 32 millimeters. What is the approximate height of the pick? Solution Draw the equilateral triangle described. A B C Its altitude forms the longer leg of two ___-___- 90 triangles. The length h of the altitude is approximately the height of the pick.

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**Special Right Triangles**

5.1 Special Right Triangles Example 3 Find lengths in a 30o – 60o – 90o triangle Find the values of x and y. Write your answer in simplest radical form. Solution Step 1 Find the value of x. Substitute. Divide each side by ___. Multiply numerator and denominator by ___. Multiply fractions.

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**Special Right Triangles**

5.1 Special Right Triangles Example 3 Find lengths in a 30o – 60o – 90o triangle Find the values of x and y. Write your answer in simplest radical form. Solution Step 2 Find the value of y.

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**Special Right Triangles**

5.1 Special Right Triangles Checkpoint. Find the value of the variable.

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**Special Right Triangles**

5.1 Special Right Triangles Checkpoint. Find the value of the variable.

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**Special Right Triangles**

5.1 Special Right Triangles Pg. 166, 5.1 #1-25

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