   Chapter 5.6, Problem 22E 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

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 ¯ ? 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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