Chapter 5.6, Problem 16E

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

Elementary Geometry For College St...

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

Given: U T → bisects ∠ W U V , W U = 9 , U V = 12 , W V = 9 Find: W T

To determine

To find:

WT.

Explanation

Given:

UTâ†’ bisects âˆ WUV, WU=9,UV=12,WV=9.

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: UTâ†’ bisects âˆ WUV.

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

â‡’TVWT=UVWU

We know that if ab=cd then a+bb=c+dd.

â‡’TV+WTWT=UV+WUWU

From the figure, we see that, TV+WT=WV

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