Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 10 - Review Exercises - Page 491: 34

Answer

If the diagonals are congruent, then the trapezoid is isosceles.

Work Step by Step

We draw the trapezoid at the origin, giving the equal sides a length of a. We then draw the diagonals. This creates two triangles, which share a common side, which is congruent to itself by identity. Additionally, since the two sides have length a, they are congruent. Finally, they have congruent angles, they are congruent by SAS. Thus, since CPCTC, the diagonals are congruent.
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