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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 5.3, Problem 21E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercises 17 to 24, complete each proof.

Given: R Q M N = R S N P = Q S M P

Prove: ∠ N ≅ ∠ R

Chapter 5.3, Problem 21E, In Exercises 17 to 24, complete each proof. Given: RQMN=RSNP=QSMP Prove: NR PROOF Statements Reasons

PROOF
Statements Reasons
1. ?
2. ?
3. ?		 1. Given
2. S S S ∼
3. CASTC

To determine

To prove:

The statement ∠N≅∠R if the proportions are given RQMN=RSNP=QSMP.

Explanation

Definition:

SSS ∼:

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 RQMN=RSNP=QSMP.

The given figure is shown below.

Figure

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

The above mentioned SSS∼ 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, ΔMNP∼ΔQRS

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