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Understanding Special Right Triangles: 30-60-90 and 45-45-90 Theorems

This text outlines the properties of special right triangles, specifically the 30-60-90 and 45-45-90 triangles. For a triangle with angles measuring 30º, 60º, and 90º, the side lengths are represented as x, x√3, and 2x. The example shows how to find the lengths JK and HK. In the case of a triangle with angles of 45º, 45º, and 90º, the sides are x, x, and x√2. An additional example involves finding the length of side MP in square MOPR. These theorems are essential for solving problems related to triangle side lengths.

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Understanding Special Right Triangles: 30-60-90 and 45-45-90 Theorems

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  1. Geometry Vocabulary 9.7Special Right Triangles • Theorem 72: In a triangle whose angle measures are 30º-60º-90º, the lengths of the sides opposite those angles can be represented by x, x√3, and2x respectively.

  2. Example • Find JK and HK.

  3. Theorem 73 • In a triangle whose angle measures are 45º-45º-90º, the lengths of the sides opposite those angles can be represented by x, x and x√2 respectively.

  4. Example • MOPR is a square. Find MP.

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