Elementary Geometry for College Students (5th Edition)

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

Chapter 1 - Section 1.3 - Early Definitions and Postulates - Exercises: 28b


$\overline{AC}$ $\cong$ $\overline{BD}$

Work Step by Step

In part (a) we determined that the three segments, $\overline{AB}$, $\overline{BC}$, and $\overline{CD}$, are all congruent to each other. Therefore, $\overline{AB}$ $\cong$ $\overline{BC}$ $\cong$ $\overline{CD}$. Using the Segment Addition Postulate (twice), $\overline{AB}$ + $\overline{BC}$ $\cong$ $\overline{CD}$, and $\overline{BC}$ + $\overline{CD}$ $\cong$ $\overline{BD}$. If $\overline{AB}$ + $\overline{BC}$ $\cong$ $\overline{BC}$ + $\overline{CD}$, then $\overline{AC}$ $\cong$ $\overline{BD}$.
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