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Elementary Geometry for College St...

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

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BuyFindarrow_forward

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 ¯

Chapter 3.2, Problem 18E, In Exercise 17 to 20, first prove that triangles are congruent then use CPCTC. Given: M is the

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. NMPQMR 4. If two lines intersects, the vertical angles formed are .
5. PR and NQ 5. If two parallel lines are cut by a transversal, then the alternate interior angles will be congruent.
6. ΔNMPΔQMR 6

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