Chapter 4.4, Problem 26E

### 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 the figure, a | | b | | c and B is the midpoint of A C ¯ . If A B = 2 x + 3 y , B C = x + y + 7 and D E = 2 x + 3 y + 3 and E F = 5 x − y + 2 , Find x         a n d           y .Exercises 25, 26

To determine

To Find:

The value of xandy.

Explanation

The given diagram is

Given: a||b||c and B is the midpoint of ACÂ¯.

Also, AB=2x+3y, BC=x+y+7 and DE=2x+3y+3 and EF=5xâˆ’y+2.

We know that, when three or more parallel lines intercept congruent line segments on one transversal, then they intercept congruent line segments on any transversal.

Therefore, ABâ‰…BCâ€Šandâ€ŠDEâ‰…EF.

Now, 2x+3y=x+y+7.

It becomes 2x+3yâˆ’xâˆ’y=7.

Then x+2y=7.

Therefore, x=7âˆ’2y

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