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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Exercises 18 and 19 are based on a theorem ( not stated) that is the converse of Theorem 5.6.3. See the figure on above.

Given: N P = 4 , M N = 8 , P Q = 3 , and M Q = 6 ; m P = 63 and m M = 27
Find: m P N Q
(HINT: N P M N = P Q M Q . )
Chapter 5.6, Problem 18E, Exercises 18 and 19 are based on a theorem  not stated that is the converse of Theorem 5.6.3. See

To determine

To find:

mPNQ.

Explanation

Given:

NQ bisects MNP, NP=4,MN=8,PQ=3,MQ=6,mP=63,mM=27.

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.

NPMN=PQMQ

In a triangle the sum of the angles is 180.

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