Question

Unscramble the proof so that the statements on the left match up to the justifications on the right. It also needs to be in the correct order.

Answer 1

Really need help with this, please!

Answer 2

There area couple parts that are fairly easy. Can you tell me what the very first statement and reason is?

Answer 3

a). Angles 2 and 5 are supplementary - Given.

Answer 4

Perfect. Next up, we need to find a statement that logically follows from "Angles 2 and 5 are supplementary." Do you have any guesses to this?

Answer 5

<2 + <5 = 180 ?

Answer 6

Right again. The reasoning for this, is merely the definition of supplementary angles. Now it get's a little bit trickier. Any guesses for the third statement?

Answer 7

<2 = <3 - Vertical Angle Theorem ?

Answer 8

Right again! So we have half of the statements and reasons in the correct order. We just have a couple more to go. For the fourth statement, we know

<2+<5=180, and <2=<3

What should be the next statement?

Answer 9

Either <3 + <5 = 180
or Angle 3 and angle 5 are supplementary.

Answer 10

It certainly must be one of those two. In fact, it should be that "<3 + <5 = 180." Can you give the reasoning?

Answer 11

Using my vast deduction skills (jokes), I'd say it would be Definition of Supplementary Angles.

Answer 12

Close. I would argue for "substitution." Note that since you have the two facts "<2+<5=180," and "<2=<3" it's merely a substitution to get "<3 + <5 = 180."

Now, I'm sure you can tell me the next reason.

Answer 13

Angle 3 and angle 5 are supplementary - Definition of Supplementary Angles

line l || line m - Converse of Same-Side Interior Angles Theorem

Answer 14

Perfect!

Answer 15

Thanks so much @KingGeorge! You're the best :D

Answer 16

You're welcome.