Chapter 5.2, 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 that rectangle A B C E is similar to rectangle M N P R and that △ C D E ∼ △ P Q R , what can you conclude regarding pentagon A B C D E and pentagon M N P Q R ?

To determine

To find: What can you conclude regarding pentagon ABCDE and pentagon MNPQR.

Explanation

Given:

The rectangle ABCE is similar to rectangle MNPR and Î”CDEâˆ¼Î”PQR.

Definition used:

Two polygons are similar if and only if two conditions are satisfied:

1. All pairs of corresponding angles are congruent.

2. All pairs of corresponding sides are proportional.

Calculation:

We have Î”CDEâˆ¼Î”PQR.

Thus the corresponding angles are congruent and the corresponding sides are proportional.

That is mâˆ D=mâˆ Q,mâˆ DEC=mâˆ QRP,mâˆ DCE=mâˆ QPR and

DCQP=DEQR=ECRPÂ Â ...(1)

Also we have rectangle ABCE is similar to rectangle MNPR.

Thus the corresponding angles are congruent and the corresponding sides are proportional.

That is, mâˆ CEA=mâˆ PRM,mâˆ ECB=mâˆ RPN,mâˆ A=mâˆ M, mâˆ B=mâˆ N and

AEMR=ABMN=BCNP=ECRPÂ Â Â

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