Chapter 5.6, Problem 23E

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

In Δ A B C , A C = 5.3 , B C = 7.2 and B A = 6.7. With 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:

Which line segment is longer

AE¯ or EC¯?

Explanation

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,

AC=5.3,BC=7.2â€‰andâ€‰BA=6.7

From Angle-Bisector theorem,

In Î”ABC

ECBC=EABA.........(1)

Let EC=x,

EA=CAâˆ’CE......(2)

Substitute EC=x and AC=5.3 in equation (2) we get,

EA=5.3âˆ’x

Substitute EA=5.3âˆ’x,BC=7.2â€‰andâ€‰BAâ€‰=â€‰6

To determine

b)

To find:

Which line segment is longer

CD¯ or DB¯

To determine

c)

To find:

Which line segment is longer

AF¯ or FB¯

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