   Chapter 3.2, 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 Exercise 17 to 20, first prove that triangles are congruent then use CPCTC. Given: M is the midpoint of N Q ¯ N P ¯ ∥ R Q with transversal P R ¯ and N Q ¯ Prove: N P ¯ ≅ Q R ¯ To determine

To prove:

The given statement.

Explanation

Given:

The following figure shows the given diagram.

Given that,

M is the midpoint of NQ¯ and NP¯RQ with transversal PR¯ and NQ¯.

Approach:

By definition of ASA, if two angles and their included side of one triangle is congruent to two angles and their included side of second triangle, then triangle will be congruent.

The completed proof is shown in the following table.

 PROOF Statements Reasons 1. M is the midpoint of NQ¯ 1. Given 2. NM¯≅MQ¯ 2. The midpoint of a segment forms two ≅ segments. 3. NP¯∥RQ with transversal PR¯ and NQ¯ 3. Given 4. ∠NMP≅∠QMR 4. If two lines intersects, the vertical angles formed are ≅. 5. ∠P≅∠R and ∠N≅∠Q 5. If two parallel lines are cut by a transversal, then the alternate interior angles will be congruent. 6. ΔNMP≅ΔQMR 6

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