Geometry: Common Core (15th Edition)

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

Chapter 5 - Relationships Within Triangles - 5-2 Perpendicular and Angle Bisectors - Lesson Check - Page 296: 3

Answer

$DC = 18$

Work Step by Step

According to the perpendicular bisector theorem, points lying on the perpendicular bisector of a segment are equidistant from the segment's endpoints. In the diagram, we see that $\overline{CE}$ is the perpendicular bisector of $\overline{BD}$; therefore, $C$ is equidistant from $B$ and $D$. $DC$, thus, is equal to $BC$, so if $BC = 18$, then $DC = 18$.
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