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Special Right Triangles

Special Right Triangles. Lesson 9.7. 30 º-60º-90º Triangles. Theorem 72 : In a triangle whose angles have the measures of 30 º , 60 º , and 90 º , the lengths of the sides opposite these angles can be represented by x, , and 2x respectively. (30 º-60º-90º-Triangle Theorem). 3 0 º. 2x.

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Special Right Triangles

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  1. Special Right Triangles Lesson 9.7

  2. 30º-60º-90º Triangles Theorem 72: In a triangle whose angles have the measures of 30º, 60º, and 90º, the lengths of the sides opposite these angles can be represented by x, , and 2x respectively. (30º-60º-90º-Triangle Theorem) 30º 2x 60º x

  3. Find BC and AC. • Place x, , and 2x on the diagram. • 2x = 10x = 5 • BC = 5 • AC = A 2x = 10 10 C 60º B x

  4. 45º-45º-90º Triangles Theorem 73:In a triangle whose angles have the measures of 45º, 45º, and 90º, the lengths of the sides opposite these angles can be represented by x, x, and , respectively. (45º-45º-90º-Triangle Theorem) x 45º x 45º

  5. MOPR is a square. Find MP. • The diagonal divides the square into two 45º-45º-90º triangles. • Place x, x, and on the corresponding parts of the triangle. • Since x = 9, • MP = R M 9 x = 9 O P x

  6. Find ST and TV. • Place x, x, and onto the diagram. T x S x 4 V 45º

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