Question

Finish the proof? I can't get the last one :/

Answer 1

so far I have:

Given
Vertical Angles
Same side interior angles
_________

Answer 2

It's been a long time since I've done proofs like this, but it looks like you can say that angles 2 and 3 are congruent.

Then since angles 2 and 3 are congruent, angles 3 and 5 must be supplementary.

And since the same side interior angles are supplementary, that implies that l and m are parallel.

Answer 3

So if I were going to write it out like

Answer 4

you there?

Answer 5

1. Vertical Angle Theorem
2. <3+<5=<2+<5=180 degrees (something like that, I forget the exact wording you need here, sorry)
3. Interior Angles Theorem

Answer 6

ok ^.^ thanks

Answer 7

You're welcome!

Answer 8

Could you help me with one more thing?

Answer 9

Sure

Answer 10

Part of the sentence looks like it is cut off... Is there anything after "Suppose that..." and before "...m<2=180..."?

Answer 11

Yeah sorry it's "suppose that m<1 + m/2 = 180"

Answer 12

i meant \ for m\2 not m<2

Answer 13

o.O

Answer 14

Ok.

Since <1+<2=180 the two streets must be parallel by the interior angles theorem.

Let me see if I can prove it...

I'm going to call <3 the other angle that is supplementary to <1 on the interior of the two streets, and <4 the vertical angle of <2

1. <1+<2 =180 - Given
2. <1 and <2 are supplementary - Definition of supplementary angles
3. <1+<3=180 - Given that Maple St. is a straight line
4. <1 and <3 are supplementary - Definition of supplementary angles
5. <2 = 180 - <1 - Subtraction Property of Equality
6. <3 = 180 - <1 - Subtraction Property of Equality
7. <2 and <3 are congruent - Definition of congruent angles
8. <2 and <4 are congruent - Vertical Angle Theorem
9. <4 and <3 are congruent - Transitive Property of Equality
10. Maple St. and Elm St are then parallel - Corresponding Angles Postulate

Answer 15

Sorry that took so long.

Answer 16

Thanks