Question

Hi(: Could someone check this two column proof and help me write a paragraph proof for it?
<2 and 5< are supplementary | Given
<2 is congruent to <3 | Vertical angle theorem
<2+<5=180* | definition of supplementary angles
<3+<5=180* | definition of supplementary angles
<3 and <5 are supplementary | substitution
line l || line m | converse of the same side interior angle theorem

Answer 1

Given: Angles 2 and 5 are supplementary.

Prove: lines l and m are parallel.

Answer 2

@soulflower

I think the 2-column proof needs a wee bit of work.

Here is what I got using your steps which are correct.

1) <2 and 5< are supplementary | Given

2) m<2+m<5=180 | definition of supplementary angles

3) <2 is congruent to <3 | Vertical angle theorem

4) m<2 = m<3 | Definition of congruent angles

5) m<3 + m<5 =180 | Substitution

6) < 3 and <5 are supplementary | Definition of Supplementary Angles

7) line l || line m | converse of the same side interior angle theorem


So, take a look at that before working on the paragraph proof.

Note: You could argue that < 2 and < 5 are supplementary, then <5 and <6 are supplementary, after which you would conclude that <2 is congruent to <6 because supplements of congruent angles are congruent. Then, you could get the lines parallel using the converse of the corresponding angles postulate.