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

This section covers the properties of special right triangles: 45°-45°-90° and 30°-60°-90°. In a 45°-45°-90° triangle, the hypotenuse is √2 times the length of the legs. For a 30°-60°-90° triangle, the hypotenuse is twice the shorter leg, and the longer leg is √3 times the shorter leg. We will find side lengths based on given legs or hypotenuses, ensuring a solid grasp of these important geometric concepts. Practice problems are included to reinforce learning and application of these theorems.

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

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  1. GeometrySection 7.4 Special Right Triangles

  2. Formed by cutting a square in half. 45°-45°-90° Triangle n n

  3. 45°-45°-90° Triangle Theorem • In a 45°-45°-90° triangle, the hypotenuse is times as long as the legs

  4. Find the lengths of the sides of a 45°-45°-90° Triangle • Find the length of the hypotenuse of a triangle with leg lengths of 8. • Find the length of the hypotenuse of a triangle with leg lengths of • Find the length of the legs of a triangle with an hypotenuse of

  5. Given an equilateral triangle with side lengths of 2: 30°-60°-90° Triangle

  6. 30°-60°-90° Triangle Theorem • In a 30°-60°-90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg

  7. Find the lengths in a 30°-60°-90° triangle • Find the length of a leg, if the shorter leg is 2, and the hypotenuse is 4. • Find the length of the hypotenuse and longer leg if the shorter leg is

  8. Assignment • Section 7.4 • Page 461 • Problems # 4-18 even, 24, 28

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