Question

Use a paragraph proof to prove:

If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.

Answer 1

Corresponding angles of parallel lines are equal, so ∠1=∠5, ∠2=∠6,...
The sum of angles on a straight line is 180, hence ∠4=180-∠1
As ∠1=∠5, thus ∠4=180-∠5, hence interior angles on same side are supplementary.

Answer 2

thx @agostino, could u help me with another one if you don't mind

Answer 3

k

Answer 4

Use a paragraph proof to prove:

If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.

Answer 5

First, we know that for parallel lines, they have their corresponding angles equal.

This means if ∠2=∠6=180-∠3, then AB//CD.

Answer 6

@agostino is that I all I need to know for that problems, so its done

Answer 7

You can always try to seek more rigorous proofs if you want. You can create one too. :)

Answer 8

thx @agostino

Answer 9

No prob