Short Answer

Question

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Write a paragraph proof of Theorem 3-8: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

The information and diagram for a two column proof is shown.

Answer 1

Given: Line n is perpendicular to lines p and q
Prove: Line p is parallel to line q

Statement | Reason

1. Line n is perpendicular to line p | Given
2. Line n is perpendicular to line q | Given
3. ∠1 and ∠2 are right angles | Definition of perpendicular lines
4. ∠1 ≅ ∠2 | All right angles are congruent
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5. Line p is parallel to line q | If two angles are congruent and one pair of corresponding sides are concurrent, then the two lines are parallel (Alternate Interior Angles Theorem)

Therefore, we have proved that if two lines are perpendicular to the same line, then they are parallel to each other.