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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鈭�n

Given

2.鈭�2鈮�鈭�1鈬�m鈭�2=m鈭�1

Alternate interior angle

3.m鈭�2+m鈭�4=180

Linear pair

4.m鈭�1+m鈭�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

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

鈭�1and 鈭�2forms a pair of alternate interior angles

鈭�4and 鈭�2 forms a linear pair

03

Step 3. Write two column proof

The proof in two column form is

Statement

Reason

1.k鈭�n

Given

2.鈭�2鈮�鈭�1鈬�m鈭�2=m鈭�1

Alternate interior angle

3.m鈭�2+m鈭�4=180

Linear pair

4.m鈭�1+m鈭�4=180

Substitution Property

Hence 鈭�1is supplementary to 鈭�4 proved

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Most popular questions from this chapter

If a鈭�b, name all angels that must be congruent to 鈭�1.

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