Question

Examine the paragraph proof. Which theorem does it offer proof for?

Segments JK and HI are parallel, segment LO intersects segment JK at point N, segment LO intersects segment HI at point M, and points N and M are between points L and O on segment LO.

Prove: ∠JNL ≅ ∠HMN

According to the given information, segment JK is parallel to segment HI and points L, N, M, and O all lie on the same line. The measure of ∠LNM 180° by the definition of a straight angle. Because ∠JNL and ∠JNM are adjacent to one another, the Angle Addition Postulate allows the measure of ∠JNL and ∠JNM to equal the measure of ∠LNM. Through the Substitution Property of Equality, the measure of ∠JNL plus the measure of ∠JNM equals 180°. Since ∠JNM and ∠HMN are same-side interior angles, the measure of ∠JNM plus the measure of ∠HMN equals 180°. Using substitution again, the measure of ∠JNL plus the measure of ∠JNM equals the measure of ∠LNM plus the measure of ∠HMN. Finally, the Subtraction Property of Equality allows the measure of ∠JNM to be subtracted from both sides of the equation. The result is that the measure of ∠JNL is the same as the measure of ∠HMN. Because their angle measures are equal, the angles themselves are congruent by the definition of congruency.

Answer 1

I need to know something. Have you tried drawing the points for L, N, M, and O? And how JK is parallel to HI, yet?

Answer 2

And also, if there are multiple-choice options. I'm gonna need those.

Answer 3

I'll wait for your response. I think I have it all organized.

Answer 4

Alternate Interior Angles Theorem
Corresponding Angles Theorem
Vertical Angles Theorem
Same-Side Interior Angles Theorem

Answer 5

Those are the options

Answer 6

I have tried drawing them, It didnt look good... it was in my notebook too, and I dont know how to take a picture and upload it on here

Answer 7

If you're on PC, trying using the snipping tool. It's a desktop app and should always be on it if you're using windows

Answer 8

It's literally called Snipping Tool

Answer 9

Im on PC but It was in my actual physical notebook

Answer 10

like, pen and paper, and I dont know how to-

Answer 11

Oh- HM. Uh- if you have a phone, try taking a picture on it

Answer 12

or something like that, and then QC has an app that you can download

Answer 13

You could do it that way?

Answer 14

nope-

Answer 15

The big sigh. Alright, I think I can figure this out. IT's k. Let me show you what I ended up drawing for the first part though, and you can compare images.

Answer 16

okay. I just want to thank you for being so patient. I know Im difficult to work with.

Answer 17

That took me a while to draw. And you're welcome, the common vertex that I think is right = M. But with the information that I gathered, I may have to re draw it

Answer 18

Hold on, I need to finish some of my work then I'll come back to you. Alright? If dude is available and I don't respond you can ping him.

Answer 19

Okay, thanks for your help!

Answer 20

@dude

Answer 21

prove : ∠JNL ≅ ∠HMN

hope this image will help you

Answer 22

thats what my image looked like\