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Chapter 3: Q21 (page 82)

Write proofs in two-column form.

Given: k鈭�l

Prove: 鈭�1is supplementary to 鈭�7

Short Answer

Expert verified

Proof in two column form is

Statement

Reason

1.k鈭�l

Given

2.鈭�4鈮�鈭�7

Vertically opposite angle

3.m鈭�1+m鈭�4=180

Same side interior angle

4.m鈭�1+m鈭�7=180

Substitution Property

Step by step solution

01

Step 1. Observations from figure

Line tis transversal to the parallel lines kandI

02

Step 2. Vertically opposite angle

鈭�4and 鈭�7are vertically opposite angles, so they are congruent

鈭�4鈮�鈭�7m鈭�4=m鈭�7

03

Step 3. Same-side interior angles

鈭�1and 鈭�4forms a pair of same-side interior angles

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

m鈭�1+m鈭�4=180 (1)

04

Step 4. Use substitution property

Substitute m鈭�7for m鈭�4in equation (1)

m鈭�1+m鈭�7=180

Thus, proof in two column form is

Statement

Reason

1.k鈭�l

Given

2.鈭�4鈮�鈭�7

Vertically opposite angle

3.m鈭�1+m鈭�4=180

Same side interior angle

4. m鈭�1+m鈭�7=180

Substitution Property

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Most popular questions from this chapter

Write proof in two column form

Given: k鈭�l

Prove: 鈭�2鈮�鈭�7

Classify each pair of angles as alternate interior, same side interior

or corresponding angles

and

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