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HACTEHA [7]
2 years ago
5

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.
Mathematics
1 answer:
lisabon 2012 [21]2 years ago
6 0

To enable the completion of the proof that line <em>l</em> is parallel to line <em>m</em>, 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. <u>Definition of supplementary ∠s</u>

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

4. <u>m∠1 + m∠3 = 180° </u>    {}                                4. <u>Definition of supplementary ∠s</u>

5. m∠1 + m∠2 = m∠1 + m∠3      {}                   5. <u>Transitive property of equality</u>

6. <u>m∠2 = m∠3 </u>     {}                                        6. <u>Subtraction property of equality</u>    

7. l ║ m      {}                                                   7. <u>Converse of alternate interior </u>

    {}                                                                      <u>angles postulate</u>

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 <em>x</em> = <em>y</em>, and <em>z </em>= <em>y</em>, then <em>x</em> = <em>z</em>.

  • 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.

Learn more here:

brainly.com/question/25178453

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