## Geometry: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 8 - Right Triangles and Trigonometry - 8-1 The Pythagorean Theorem and It's Converse - Practice and Problem-Solving Exercises - Page 496: 26

#### Answer

Yes $33^{2}$+$56^{2}$=$65^{2}$

#### Work Step by Step

The Pythagorean Theorem says the $(leg_{1})^{2}$+$(leg_{2})^{2}$=$hypotenuse^{2}$. If this is true, then a triangle is a right triangle. This formula is more commonly referred to as $a^{2}$+$b^{2}$=$c^{2}$ You are given the lengths of the legs as 33 and 56. You are given the length of the hypotenuse as 65. Substitute 33 in for a, 56 in for b, and 65 in for c. $a^{2}$+$b^{2}$=$c^{2}$ $33^{2}$+$56^{2}$=$65^{2}$ 1089+3136=4225 4225=4225

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