Question

In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that lines l and m are parallel. Angles 1 and 2 are supplementary by definition. Upload the entire proof below.
Given:
∠1 and ∠2 are supplementary angles
Prove:
l || m



STATEMENT REASON
1.∠1 and ∠2 are supplementary angles 1. Given
2. m∠1 + m∠2 = 180° 2.
3. ∠1 and ∠3 are supplementary angles 3. Exterior sides in opposite rays
4. 4.
5. m∠1 + m∠2 = m∠1 + m∠3 5.
6. 6.
7. l || m 7.

Answer 1

To enable the completion of the proof that line l is parallel to line m, a

diagram showing the lines and their common transversal is attached.

The completed two column proof is presented as follows;

Statement  ${}$                                                      Reason

1. ∠1 and ∠2 are supplementary angles  ${}$   1. Given

2. m∠1 + m∠2 = 180°   ${}$                                 2. Definition of supplementary ∠s

3. ∠1 and ∠3 are supplementary angles  ${}$  3. Exterior sides in opposite rays  

4. m∠1 + m∠3 = 180°    ${}$                                4. Definition of supplementary ∠s

5. m∠1 + m∠2 = m∠1 + m∠3      ${}$                   5. Transitive property of equality

6. m∠2 = m∠3     ${}$                                        6. Subtraction property of equality    

7. l ║ m      ${}$                                                   7. Converse of alternate interior

    ${}$                                                                      angles postulate

Reasons:

• Reason for statement 2: Supplementary angles are defined as two angles that sum up to 180°

• Reason for statement 3: Two angles are supplementary if the exterior sides that form each angle are opposite rays (rays that are drawn out infinitely in opposite direction but have the same endpoint)

• Statement 4: Mathematical expression of the sum of ∠1 and ∠3; Reason for statement 4 is the definition of supplementary angles

• Reason for statement 5: Transitive property of equality describes the property that if a number x = y, and z = y, then x = z.

• Statement 6: Subtracting m∠1 from both sides of the equation in statement 5. gives; m∠1 + m∠2 - m∠1 = m∠1 + m∠3 - m∠1 ⇒ m∠2 = m∠3. Reason for statement 6 is the subtraction property of equality

• Reason for statement 7: The converse of the alternate interior angles postulate states that if the alternate interior angles formed between two  lines and a common transversal are congruent, the two lines are parallel.

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