Question

Please help! I don't get this at all...
If and ∠ 1 ≅ ∠ 2, prove that ∠ NLO ≅ ∠ NPM.

Where is Hector's mistake and how must he correct it?

Answer 1

https://grantsburg.brainhoney.com/Resource/14634238,275,0,1E/Assets/58639_51dc42ec/05_07_6a.jpg

Answer 2

Statement 1 because the information in the proof is not given in the problem.
Statement 3 because the angle addressed is irrelevant to the proof.
Statement 4 because the triangles are inaccurately labeled.
Statement 5 because those angles are not corresponding parts.

Answer 3

Statements Reasons
1. LN ~ NP Given
2. ∠ 1 ≅ ∠ 2 Given
3. ∠ Q ≅ ∠ Q Reflexive Property
4. ΔLNO ≅ ΔPNM Angle-Angle-Side Postulate
5. ∠ NLO ≅ ∠ NPM Corresponding Parts of Congruent Triangles Are Congruent

Answer 4

Well, we can say:
\[
\angle 1 = \angle 2 = \alpha
\]

Now for both triangle △NLO we can say:
\[
\angle L = 180^\circ - ( \angle N + \angle 2) = 180^\circ - (\angle N + \alpha)
\]
and for triangle and △NPM we can say:
\[
\angle P = 180^\circ - ( \angle N + \angle 1) = 180^\circ - (\angle N + \alpha)
\]

Therefore ∠L≅∠P

And for the other part, first you didn't say anything about LN or NP so I would say A for using information that is not given in the problem.
He also uses angle ∠Q that is in neither one of those triangles in his triangle congruence claim. So I would say that B for addressing irrelevant angles to the proof.