Question

Use a paragraph proof to prove the converse of the same-side interior angles theorem.

Given: Same-side interior angles are supplementary

Prove: segment A B is parallel to segment C D.

Transversal EF cuts through parallel line segments AB and CD, creating four sets of corresponding angles; angles 1, 2, 3, 4 are formed by EF and AB; angles 5, 6, 7, 8 are formed by EF and CD.

Answer 1

@e.mccormick
Hi! Is there any way you can help me? :)

Answer 2

OK, so you basically need to write out the proof in text. Hmm.

Answer 3

One way to start is to work out a diagram. This can help you keep things straight. If you can understand t without the diagram, fine. But with it, it can be easier to keep track of what you are describing.

Answer 4

You are allowed to use the fact that on a line, "Same-side interior angles are supplementary." With that diagram, you therefore know that 1+2=180 degress, and 1+4=180 degrees. This means you can prove opposite angles. You need to keep working like that until you show that 2=6, 5=1, etc.

Does that give you a good place to go with this and why?

Answer 5

Be aware that because this is a paragraph, you need to describe the physical proximity of the angles. For example, in my drawing 1 next to 2 and 4, but opposite 3, it a textual description. Adding that 3 and 4 are on the side of AB that is closes to CD also clarifies this more. So I am describing the picture and then using the law have been left with to prove other laws which end in the lines never crossing, which means they are parallel.

Also, at the end of a proof it is customary to put q.e.d., //, or \(\blacksquare\).