Question

Time Elapsed: HieAttempt due: Jun 20 a40 Minutes, 30 SeGiven: 21 and 23 are supplementaryProve: line m || linenComplete the proof. Number your reasons in the textbox below.Reasons1.2.Statements21 and 23 are supplementary21 + 23 = 18022 = 23Z1 + Z2 = 180°21 and 22 are supplementaryline m || linen3.4.5.6.

Answer 1

Statements and reasons.

1) ∠1 and ∠3 are supplementary

Reason: This is true because it is stated in the question.

2) ∠1 + ∠3 = 180º

Reason: By statement 1, ∠1 and ∠3 are supplementary, and by definition, supplementary angles sum up 180º.

3) ∠2 = ∠3

Reason: From the picture we see that ∠2 and ∠3 are opposite congruent angles, so they are equal.

4) ∠1 + ∠2 = 180º

Reason: from statement 2 we have ∠1 + ∠3 = 180º, and from statement 3 we have ∠2 = ∠3, so we have ∠1 + ∠2 = 180º.

5) ∠1 and ∠2 are supplementary

Reason: from statement 4 we have that ∠1 sum up ∠2, so by definition ∠1 and ∠2 are supplementary.

6) line m || line n

Reason: from the picture we see that ∠1 and ∠2 are internal collateral angles of the lines m and n, and from statement 5 we know that ∠1 and ∠2 are supplementary, so we have that the angle between line m and line n is 180°, and by definition, they are parallel lines.

Summary of the reasons

1) It is stated in the question

2) By statement 1 and by definition of supplementary angles.

3) Because they are opposite congruent angles, so they are equal.

4) By statement 2 and 3.

5) By statement 4, and by definition of supplementary angles.

6) By picture ∠1 and ∠2 are internal collateral angles of the lines m and n, and by statement 5 they are supplementary so they are parallel lines.