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Geometry Lesson 8.2 Special Right Triangles Name __________________________________ Let’s take a look at isosceles right triangles. What are the measures of the angles of any isosceles right triangle? ______, _______, _______ Find the length of the hypotenuses of the following isosceles right triangles. x 2 22 22 x 2 32 32 x2 8 x 2 18 x 82 2 x 18 3 2 Therefore, to find the hypotenuse of an isosceles right triangle, simple multiply a leg by ________. Theorem 8-5: 45°-45°-90° Triangle Theorem: In a 45°-45°-90° triangle, both legs are ______________ and the length of the hypotenuses is _______ times the length of a _______. hypotenuse 2 leg Thus, leg hypotenuse 2 Read the following examples and then use them to help you with the practice problems. Examples: Find the value of each variable. hypotenuse 2 leg h 29 h9 2 a) hypotenuse 2 leg x 22 2 x 2 2 x4 b) Practice: Find the values of the variables. 1) 2) 5) 6) leg c) z 4) 7) 4 2 2 z4 3) hypotenuse 2 Now, let’s take a look at right triangles with acute angles of measures 30° and 60°. Theorem 8-6: 30°-60°-90° Triangle Theorem: In a 30°-60°-90° triangle, the length of the ________________ is ___________ the length of the shorter leg. The length of the ___________ leg is ______ times the length of the shorter leg. longer leg = 3 shorter leg hypotenuse = 2 shorter leg Read the following examples and then use them to help you with the practice problems. Examples: Find the values of the variables. longer leg 3 shorter leg hypotenuse 2 shorter leg d) 8 2 x y 3 x 4x hypotenuse 2 shorter leg f 2 d longer leg 3 shorter leg e) 5 3 3 d 5d 11) f 2 5 10 Practice: Find the values of the variables. 8) y4 3 9) 10) 12) PUT IT TOGETHER!! Practice: Find the values of the variables. 13) 14) 15)