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Chapter 3: Q22 (page 82)

Copy what is shown for Theorem 3-3 on page 79. Then write a proof in two-column form.

Short Answer

Expert verified

Proof in two column form is

Statement

Reason

1.k∥n

Given

2.∠2≅∠1⇒m∠2=m∠1

Alternate interior angle

3.m∠2+m∠4=180

Linear pair

4.m∠1+m∠4=180

Substitution Property

Step by step solution

01

Step 1. Copy what is shown for Theorem 3-3 on page 79

Line t is transversal to the parallel lineskandn

02

Step 2. Observe from figure

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

∠1and ∠2forms a pair of alternate interior angles

∠4and ∠2 forms a linear pair

03

Step 3. Write two column proof

The proof in two column form is

Statement

Reason

1.k∥n

Given

2.∠2≅∠1⇒m∠2=m∠1

Alternate interior angle

3.m∠2+m∠4=180

Linear pair

4.m∠1+m∠4=180

Substitution Property

Hence ∠1is supplementary to ∠4 proved

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