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McGraw Hill Integrated II, 2012 View details

1. Bisectors of Triangles

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Exercise 1 Page 411

Use the Perpendicular Bisector Theorem.

XW=12

Practice makes perfect

We are given the following diagram and asked to find the measure of XW.

As we can see, 12 represents the length of the segment XY. Moreover, we see that XZ intersects WY at the midpoint Z and is perpendicular to WY. Therefore, XZ is a perpendicular bisector of WY. Let's use the Perpendicular Bisector Theorem.

Perpendicular Bisector Theorem
If a point is on the bisector of a segment, then it is equidistant from the endpoints of the segment.

By this theorem, X is equidistant from the endpoints of the segment WY. This means that XW and XY have the same measures. Therefore, we found that XW=12.