Chapter 5.CT, Problem 13CT

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# In △ M N P ,   N Q → bisects ∠ M N P . If PN = 6, MN = 9, and MP = 10, find PQ and QM.

To determine

To find:

The value of PQ and QM.

Explanation

Given, â–³MNP,

NQâ†’ bisects âˆ MNP.

PN = 6, MN = 9, and MP = 10,

By Angle-Bisector theorem:

If a ray bisects one angle of a triangle, then it divides the opposite side into segments whose length are proportional to the lengths of the two sides that form the bisected angle.

i.e. PQPN=QMMN

Let us take, PQ=x

MP=PQ+QM

QM=MP-PQ

QM=10-x

PN = 6, MN = 9, and MP = 10,

Substituting these values in the equation,

PQPN

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