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Chapter 3: Q21 (page 82)

Write proofs in two-column form.

Given: k∥l

Prove: ∠1is supplementary to ∠7

Short Answer

Expert verified

Proof in two column form is

Statement

Reason

1.k∥l

Given

2.∠4≅∠7

Vertically opposite angle

3.m∠1+m∠4=180

Same side interior angle

4.m∠1+m∠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

∠4and ∠7are vertically opposite angles, so they are congruent

∠4≅∠7m∠4=m∠7

03

Step 3. Same-side interior angles

∠1and ∠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∠1+m∠4=180 (1)

04

Step 4. Use substitution property

Substitute m∠7for m∠4in equation (1)

m∠1+m∠7=180

Thus, proof in two column form is

Statement

Reason

1.k∥l

Given

2.∠4≅∠7

Vertically opposite angle

3.m∠1+m∠4=180

Same side interior angle

4. m∠1+m∠7=180

Substitution Property

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Most popular questions from this chapter

Complete each statement with the word always, sometimes, or never.Two parallel lines are coplanar.

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.

and

Exercises 23-29 refer to the diagram in step 2 of exercise 22.

.Name two planes parallel toAB¯.

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

art

and

State the postulate or theorem that justifies each statement.

m∠4=m∠8
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