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 - Practice and Problem-Solving Exercises - Page 297: 16


$x = 12$ Both $JK$ and $JM$ are $17$.

Work Step by Step

The angle bisector theorem states that a point that is located on an angle's bisector is equidistant from the angle's sides. In this diagram, we see that $\overline{JL}$ is the angle bisector of $\angle KLM$. Therefore, $J$, which is a point on the bisector, is equidistant from the sides of the angle. So, $L$ is equidistant from $\overline{LK}$ and $\overline{LM}$. Therefore, $\overline{JK}$ is equal to $\overline{JM}$. Let's set $JK$ and $JM$ equal to one another to find the value for $x$: $x + 5 = 2x - 7$ Subtract $x$ from each side to isolate the variable on one side of the equation: $5 = x - 7$ Add $7$ to each side of the equation to solve for $x$: $x = 12$ $JK = JM = x + 5$ Plug in $12$ for $x$: $JK = JM = 12 + 5$ Add to solve: $JK = JM = 17$
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