   Chapter 5.6, Problem 17E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

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

Given: N Q → bisects ∠ M N P , N P = M Q , Q P = 8 , M N = 12 Find: N P To determine

To find:

NP.

Explanation

Given:

NQ bisects MNP, NP=MQ,QP=8,MN=12.

Theorem used:

Angle bisector theorem:

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

Calculation:

Given: NQ bisects MNP.

Then by angle-bisector theorem, the ray NQ divides the opposite side into segments whose lengths are proportional to the lengths of the two sides that form the bisected angle

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