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Math
GeometryElementary Geometry for College Students6th Edition

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

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

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
BuyFindarrow_forward

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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Chapter 3.5,
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Chapter 3.5,
Problem 31E
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