   Chapter 5.6, Problem 26E 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: M R → bisects ∠ N M P , M N = 2 x , N R = x , R P = x + 1 , and M P = 3 x − 1 Find: x

To determine

To find:

The value of x.

Explanation

Given:

MR bisects NMP, MN=2x,NR=x,RP=x+1,MP=3x1.

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:

We have MR bisects NMP.

By angle bisector theorem, we get

MNMP=RNRP.

Given that MN=2x,NR=x,RP=x+1,MP=3x1

Thus 2x3x1=xx+1

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