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: 20


$WZ = 10$

Work Step by Step

The converse of the angle bisector theorem states that a point inside an angle that is equidistant from the two sides of the angle is located on the bisector of that angle. In this diagram, we see that $\overline{WY}$ is equidistant from the two sides of $\angle TWZ$, so $\overline{WY}$ is the angle bisector of $\angle TWZ$. Corresponding parts of congruent triangles are congruent; therefore, $\overline{WT}$ and $\overline{WZ}$ are congruent, so we can set them equal to one another to find $x$: $2x = 3x - 5$ Subtract $2x$ from each side of the equation to isolate the variable on the left side of the equation: $0 = x - 5$ Add $5$ to each side to solve for $x$: $x = 5$ Now that we have the value for $x$, we can substitute it into the expression for $WZ$: $WZ = 3x - 5$ Substitute $5$ for $x$: $WZ = 3(5) - 5$ Multiply first, according to order of operations: $WZ = 15 - 5$ Solve by subtracting: $WZ = 10$
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