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I'm taking an online course and I'm a bit confused on what I'm supposed to do.

I'm not looking for someone to do my school work for me, but if someone can explain to me how I should be approaching the problem would be great.

Thanks.

edit (response to comment)

"That will require finding some other angles along the way." - This is what I'm not sure how to do. Our previous questions I've been able to use the angles of a straight line, or alternate interior angles to work out the missing angles. With this one, I'm lost on how to work out the angles here. The course material is all about writing the two column proofs. I think I'm expected to understand how to find the angles here already as it's not taught.

I don't know what the first step here should be. I can't figure out anything I can do to find another angle.

Ravenous
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  • There’s hardly a “proof” to be done here. All we have is some algebraic equations about sums of angles in several triangles. The one geometric fact is the parallelism of QP and RS. What information does that give you about angles? – Ted Shifrin Feb 04 '24 at 22:38
  • You do have alternate angles, straight angles, and vertical angles. You can put those in your two-column proof. What is $\angle STR$? – Ted Shifrin Feb 04 '24 at 22:41
  • Hint: $\angle PQS$ and $\angle QSR$ are alternate interior angles. Hopefully this helps shift something. :) – Theo Bendit Feb 04 '24 at 22:43
  • @TheoBendit that helps a lot, thank you. – Ravenous Feb 04 '24 at 22:57
  • To be direct: To what do the angles of a triangle sum? – Ted Shifrin Feb 04 '24 at 22:57

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This answers the question

How do I approach a two column geometry proof?

First work out on scrap paper why you think that angle is the size the statement claims it is. That will require finding some other angles along the way. Then organize the steps in your reasoning in "two columns" where the second column provides the geometry theorem that tells you the assertion in the first column is correct.

The text for your online course should provide examples of two column proofs. If not, a search for two column proof turns up many links.

If you really meant to ask about this particular proof, please edit the question to show us how you started and where you are stuck.

Ethan Bolker
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  • "That will require finding some other angles along the way." - This is what I'm not sure how to do. Our previous questions I've been able to use the angles of a straight line, or alternate interior angles to work out the missing angles. With this one, I'm lost on how to work out the angles here. The course material is all about writing the two column proofs. I think I'm expected to understand how to find the angles here already as it's not taught. – Ravenous Feb 04 '24 at 22:36
  • @Ravenous There are comments to the question that suggest theorems about angles that will help you. – Ethan Bolker Feb 05 '24 at 00:25