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Elementary Geometry for College St...

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

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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 Exercise 19 to 22 complete the proof.

Given: X Y ¯ Y Z ¯
1 2
Prove: M N ¯ X Y ¯

Chapter 2.3, Problem 22E, In Exercise 19 to 22 complete the proof. Given: XY  YZ 1  2 Prove: MN  XY

To determine

To find:

The complete proof of the given statement.

Explanation

Given:

The given statement is,

XY¯WZ¯ and 12.

Figure (1)

Theorem:

(1). If two lines are cut by a transversal so that two corresponding angles are congruent, then these lines are parallel.

(2). If two lines are each parallel to a third line, then these lines are parallel to each other.

Approach:

The given statement is,

XY¯WZ¯ and 12.

1 and 2 are congruent corresponding angles.

Therefore, MN¯ is parallel to WZ¯.

MN¯WZ¯ and XY¯WZ¯.

Lines MN¯ and XY¯ each are parallel to line WZ¯.

Therefore, MN¯ is parallel to line XY¯.

The complete proof of the given statement is shown in the following table,

Proof
Statements Reasons
1

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