Chapter 5.2, Problem 24E

### 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 Exercises 21 to 24, △ A D E ∼ △ A B C . Given: A D = 4 , A C = 18 , D B = A E Find: A E

To determine

To calculate:

The value of the side AE.

Explanation

Given:

Definition Used:

Similarity between Two polygons:

Two polygons are similar if and only if when all pairs of corresponding angles are congruent and all pairs of corresponding sides are proportional.

If C is a point of XYÂ¯ and Xâˆ’Câˆ’Y, then XC+CY=XY.

Calculation:

According to the definition of similar polygon, ACAE=â€‰â€‰BCDE=ABAD.

According to the segment-addition postulate, AC=AE+EC.

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