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Mastering Special Right Triangles: The 45-45-90 Triad

Learn how to solve for sides and angles in isosceles and right triangles using the 45-45-90 special triangle theorem. Practice finding hypotenuses and legs with clear examples and guided exercises.

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Mastering Special Right Triangles: The 45-45-90 Triad

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  1. Warm-up • An isosceles triangle has ________. • Find the value of x. two congruent sides 45o xo xo

  2. 7.4 Special Right Triangles Use properties of special triangles.

  3. 45o – 45o – 90o • 45o – 45o – 90o triangle is an isosceles right triangle. • It can be formed by cutting a square in half. 45o 45o 45o 45o

  4. Prove: c = Prove x = Given:

  5. Theorem 7.8: 45o – 45o – 90o Triangle Theorem • In a 45o – 45o – 90o triangle, the hypotenuse is times as a long as each leg. Hypotenuse = leg *

  6. Example 1: Find the hypotenuse in a 45o – 45o – 90o triangle a) b)

  7. Example 2: Find the legs a) b) 30 x x x x

  8. Example 3: Standardized Test Practice MNP is a right triangle. Find the length of MP. • 18 in • 36 in M 45o N P 18 in

  9. Guided Practice Find the value of the variable. 8 1) 2) 3) d 8 8 8 • Find the leg of a 45o – 45o – 90o triangle with a hypotenuse of 6.

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