Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 8 - Right Triangles and Trigonometry - 8-1 The Pythagorean Theorem and It's Converse - Practice and Problem-Solving Exercises - Page 496: 24


No $19^{2}$+$20^{2}$$\ne$$28^{2}$

Work Step by Step

The Pythagorean Theorem says that $(leg_{1}) ^{2}$+$(leg_{2})^{2}$=$hypotenuse^{2}$. 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 19 and 20. You are given the length of the hypotenuse as 28. Substitute 19 in for a, 20 in for b, and 28 in for c. $a^{2}$+$b^{2}$=$c^{2}$ $19^{2}$+$20^{2}$=$28^{2}$ 361+400=784 761$\ne$784 The sides are not equal, so it is not a right triangle.
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