   Chapter 5.3, Problem 18E ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### 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: M N ¯ ∥ Q R ¯ (See figure for Exercise 17.)Prove: Δ M N P ∼ Δ Q R P Exercises 17, 18 PROOF Statements Reasons 1. ? 1. Given 2. ∠ M ≅ ∠ R Q P 2. ? 3. ? 3. If two ∥ lines are cut by a transversal, the corresponding ∠ s are ≅ 4. ? 4. ?

To determine

To complete:

The proof by using given information.

Explanation

Given:

Given: MN¯NP¯,QR¯RP¯

Prove: ΔMNPΔQRP

 PROOF Statements Reasons 1. ? 1. Given 2. ∠M≅∠RQP 2. ? 3. ? 3. If two ∥ lines are cut by a transversal, the corresponding ∠s are ≅ 4. ? 4. ?

Definition:

AA:

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Description:

Given that MN¯QR¯.

To Prove: ΔMNPΔQRP

If two parallel lines MN and QR are cut by a transversal, the corresponding angles are congruent. Therefore, MRQP and NQRP.

From the definition of AA, the two triangles MNP and QRP are similar since two angles of one triangle are congruent to two angles of another triangle

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