Chapter 5.3, Problem 21E

### 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 17 to 24, complete each proof.Given: Q R M N = R S N P = Q S M P Prove: ∠ N ≅ ∠ R PROOF Statements Reasons 1. ?2. ?3. ? 1. Given2. S S S ∼ 3. CASTC

To determine

To prove:

The statement NR if the proportions are given QRMN=RSNP=QSMP.

Explanation

Definition:

SSS âˆ¼:

If three sides of one triangle are proportional (in length) to three corresponding sides of a second triangle, then the triangles are similar.

CASTC:

Corresponding angles of similar triangles are congruent.

Description:

Given that QRMN=RSNP=QSMP.

The given figure is shown below.

Figure

From the given figure, it is observed that QRMN=RSNP=QSMP are three sides of a triangle QRS are proportional to three corresponding sides of a triangle MNP.

The above mentioned SSSâˆ¼ definition, the two triangles MNP and QRS are similar since the three sides of one triangle are proportional to three corresponding sides of a second triangle. Hence, Î”MNPâˆ¼Î”QRS

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