   Chapter 7.CR, Problem 24CR 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: Δ A B C with medians A E , ¯ C D , ¯ B F ¯ Find: a) B G if B F = 18 b) G E if A G = 4 c) D G if C G = 4 3 To determine

a)

To find: BG if BF=18.

Explanation

Given:

The triangle ABC with medians AE¯,CD¯,BF¯.

Theorem used:

The three medians of a triangle are concurrent at a point that is two-thirds the distance from any vertex to the midpoint of the opposite side.

Calculation:

We have BF=18

By the theorem, we get BF=32BG

To determine

b)

To find: GE if AG=4.

To determine

c)

To find: DG if CG=43.

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