9.2LessonWhat You Will LearnWhat You Will LearnFind side lengths in special right triangles.Solve real-life problems involving special right triangles.Finding Side Lengths in Special Right TrianglesA 45°- 45°- 90°triangle is anisosceles right trianglethat can be formed by cutting asquare in half diagonally.Finding Side Lengths in 45°- 45°- 90°TrianglesFind the value ofx. Write your answer in simplest form.a.x845°b.xx52SOLUTION2.REMEMBERA radical with index 2is in simplest form whenno radicands have perfectsquares as factors otherthan 1, no radicandscontain fractions, andno radicals appear in thedenominator of a fraction.Previousisosceles triangleCore VocabularyCore VocabularyTheoremTheoremTheorem 9.445°- 45°- 90°Triangle TheoremIn a 45°- 45°- 90°triangle, the hypotenuse is√—2 times as long as each leg.ProofEx. 19, p. 480hypotenuse=leg⋅√—2xxx245°45°
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b.By the Base Angles Theorem (Theorem 5.6) and the Corollary to the Triangle SumTheorem (Corollary 5.1), the triangle is a 45°- 45°- 90°triangle.—√
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476Chapter 9Right Triangles and Trigonometry