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Chapter 3: Q20 (page 82)

Write proof in two column form

Given: k∥l

Prove: ∠2≅∠7

Short Answer

Expert verified

Proof in two column form is

Statement

Reason

1. k∥l

Given

2. ∠2≅∠5

Vertically opposite angle

3. ∠5≅∠7

Corresponding angle

4. ∠2≅∠7

Transitive Property

Step by step solution

01

Step 1. Observations from figure

Line tis transversal to the parallel lineskandI

02

Step 2. Vertically opposite angle

∠2and ∠5are vertically opposite angles, so they are congruent

∠2≅∠5

03

Step 3. Corresponding angles

∠5and ∠7forms a pair of corresponding angles which are congruent∠5≅∠7

04

Step 4. Use transitive property

If a=band b=cthena=c

Since, ∠2≅∠5and ∠5≅∠7implies∠2≅∠7

Thus, proof in two column form is

Statement

Reason

1. k∥l

Given

2. ∠2≅∠5

Vertically opposite angle

3. ∠5≅∠7

Corresponding angle

4. ∠2≅∠7

Transitive Property

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Most popular questions from this chapter

Complete each statement with the word always, sometimes, or never.

Two lines skew to a third line are skew to each other

Name the two lines and the transversal that form each pair of angles.

and

Draw each figure described.

Lines a and b are skew, lines b and c are skew, and a∥c.

Assume that a∥band c∥d, name all angels congruent to ∠2.

If m∠1=xwhat are the measures of the other numbered angels?
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