   Chapter 5.6, Problem 11E 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: D E ↔ ∥ B C , ¯ A D = a − 1 , D B = 2 a + 2 , A E = a , E C = 4 a − 5 Find: a  and  A D To determine

To find:

Explanation

Given:

Theorem used:

If a line is parallel to one side of a triangle and intersects other two sides, then it divides these sides proportionally.

Calculation:

Given: DEBC¯

Since if a line is parallel to one side of a triangle and intersects other two sides, then it divides these sides proportionally.

Also given that AD=a1,DB=2a+2,AE=a,EC=4a5.

Thus a12a+2=a4a5.

Now let us find the value of a.

a12a+2=a4a5(a1)(4a5)=a(2</

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