Question

Triangle LMN is an isosceles triangle with ML congruent to NL. To prove that the base angles ∠M and ∠N are congruent, LP is drawn such that point P is the midpoint of MN as shown in the diagram below. Complete the proof.

https://imgur.com/oPE9bfq

Given: ML≅NL in ∆LMN
P is the midpoint of MN

Prove: ∠M≅∠N

https://imgur.com/Xx7oZvm

A. https://imgur.com/UBffJBO

B. https://imgur.com/P3tPzMl

C. https://imgur.com/Qs90NNQ

D. https://imgur.com/MlgdASa

Answer 1

@lowkey

Answer 2

I think it’s b but I’m not sure

Answer 3

@dude

Answer 4

you're not if it's b ?

Answer 5

@silvernight269

Answer 6

It’s D

Answer 7

Without looking at the answer choices:
2. P is midpoint of MN
Then That means MP = MN
so
3. MP = MN (Definition of midpoint)

The proof in 4. says 'reflexive property of Congruence' that just means that something is equal to itself. A = A. BC = BC. Etc.

The part after that says triangle MPL = triangle NPL. And the only thing that both of them share is Line PL.
So 4. PL = PL

5. It's asking for something like SAS or SSS to prove why the triangles are congruent. We know PL = PL means a side is congruent. ML = NL means another side is congruent. MP = NP also means a side is congruent.

Sine we have 3 sides it would be SSS.
5. SSS

Answer 8

B would make the most sense so lowkey is right.