Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 3 - Section 3.3 - Isosceles Triangles - Exercises - Page 161: 49

Answer

1. Z is the midpoint of XW, so by definition, XZ is congruent to ZW. 2. We are told that XZ is congruent to YZ, so YZ is congruent to ZW. 3. Thus, both XYZ and YZW are isosceles, meaning e = a and f = d. 4. Thus, we obtain that: $2e + b = 180$ And $ 2f + 180 - b = 180$ Adding these gives: $ 2(e+f) = 180 \\ e+ f = 90$ Thus, since XYZ equals e plus f, XYZ is 90 degrees.
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