Chapter 5.6, Problem 5E

### 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: l 1 ∥ l 2 ∥ l 3 ∥ l 4 , A B = 5 , B C = 4 , C D = 3 , E H = 10 Find: E F , F G , G H (See the figure for Exercise 6.)

To determine

To find:

EF,FG,GH.

Explanation

Given:

l1âˆ¥l2âˆ¥l3âˆ¥l4 and AB=5,BC=4,CD=3,EH=10.

Theorem used:

When three (or more) parallel lines are cut by a pair of transversals, the transversals are divided proportionally by the parallel lines.

If ab=cd then a+cb+d=ab=cd.

Calculation:

Given: l1âˆ¥l2âˆ¥l3âˆ¥l4

Since when three (or more) parallel lines are cut by a pair of transversals, the transversals are divided proportionally by the parallel lines.

â‡’ABEF=BCFG=CDGH

Also given that AB=5,BC=4,CD=3,EH=10.

Thus 5EF=4FG=3GH.

We know that, if ab=cd then a+cb+d=ab=cd.

â‡’5+4+3EF+FG+GH=5EF=4FG=3GH

From the figure, we see that EF+FG+GH=EH.

â‡’5+4+3EH=5EF=4FG=3GH

Given that EH=10

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