Chapter 5.6, Problem 8E

### 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 , A B = 5 , B C = x , D E = x − 2 , E F = 7 Find: x , B C , D E

To determine

To find:

x,BC,DE.

Explanation

Given:

l1âˆ¥l2âˆ¥l3 and AB=5,BC=x,DE=xâˆ’2,EF=7.

Theorem used:

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

Calculation:

Given: l1âˆ¥l2âˆ¥l3

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

â‡’ABDE=BCEF

Also given that AB=5,BC=x,DE=xâˆ’2,EF=7.

Thus 5xâˆ’2=x7.

Now let us find the value of x.

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