Question

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

Given: Same-side interior angles are supplementary

Prove: AB || CD

Answer 1

Okay, so you know (for example) angles 5 and 5 add up to 180 (definition of supplementary). What do you know about angles 1 and 4 and why?

Answer 2

they are a linear pair

Answer 3

Which means...

Answer 4

they add up to 180

Answer 5

Okay, so if 4 and 5 add up to 180, and 4 and 1 add up to 180, when what do you know about 1 and 5?

Answer 6

they are exterior angles? not sure

Answer 7

Let's say angle 4 was 60 degrees. If 60 + angle 5 adds up to 180 and 60 + angle 1 adds up to 180, then what do you know about angles 1 and 5?

Answer 8

oh the are corresponding

Answer 9

Well, they *are* corresponding, and you do need to know that, but that's not quite what I'm looking for.

Answer 10

ah ok let me think

Answer 11

In the example I put above, what does angle 5 have to be? What does angle 1 have to be? What do you know about those two angles?

Answer 12

they are supplementary? sorry i'm lost when it comes to maths

Answer 13

It's okay. Look at the example: If 60 + angle 5 = 180, then what is angle 5?

Answer 14

120?

Answer 15

Right. And if 60 + angle 1 = 180, then what is angle 1?

Answer 16

120

Answer 17

Yes. So what do you know about angle 1 and 5?

Answer 18

they are equal

Answer 19

Yes! Okay. So you know 1 and 5 are equal. And you also said that they're corresponding. And there's a rule that says that if corresponding angles are congruent, then the lines have to be parallel. And you're done!

Answer 20

oh o so is that the paragraph

Answer 21

Well, first we found that 4 and 5 add up to 180, and that 4 and 1 add up to 180 because they're linear. Then we figured out that 1 and 5 have to be congruent. And then, because 1 and 5 are corresponding angles that are congruent, the lines have to be parallel.

Proofs are really just figuring out one thing after another after another.

Answer 22

ok can u help me with another

Answer 23

Use a paragraph proof to prove the converse of the corresponding angles postulate.

Given: Corresponding angles are congruent

Prove: AB|| CD