   Chapter 3.5, Problem 30E ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Δ M N P (not shown), point Q lies on N P ¯ so that M Q → bisects ∠ N M P . If M N < M P , draw a conclusion about the relative lengths of N Q ¯ and Q P ¯ .

To determine

To draw:

A conclusion about the relation between the length of NQ¯ and QP¯ from the given information.

Explanation

Given:

The triangle ΔMNP, point Q lies on NP¯ so that MQ bisects NMP and MN<MP.

Approach:

The angle bisector divides the opposite side in the ratio of the other two adjacent sides of the triangle.

Calculation:

Consider the triangle ΔMNP,

Figure (1)

From the given data, the side MP¯ is greater than the side MN¯.

MN¯<MP¯

Since, MQ¯ is the angle bisector of angle M and, the angle bisector divides the opposite side in the ratio of the other two sides of the triangle

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