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Elementary Geometry for College St...

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

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Δ A B C , m C A B = 80 , m A C B = 60 ,  and  A B C = 40 . With the angle bisectors as shown, which line segment is longer?

a) A E ¯ or E C ¯ ? b) C D ¯ or D B ¯ ? c) A F ¯ or F B ¯ ?
Chapter 5.6, Problem 22E, In ABC,mCAB=80,mACB=60,andABC=40. With the angle bisectors as shown, which line segment is longer? a

To determine

a)

To find:

The longer line segment, AE¯ or EC¯.

Explanation

Given:

In ΔABC, mCAB=80,mACB=60,mABC=40.

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 that mCAB=80,mACB=60,mABC=40

To determine

b)

To find:

The longer line segment, CD¯ or DB¯.

To determine

c)

To find:

The longer line segment, AF¯ or FB¯.

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