Question

If segment LN is congruent to segment NP and ∠1 ≅ ∠2, prove that ∠NLO ≅ ∠NPM: Overlapping triangles LNO and PNM. The triangles intersect at point Q on segment LO of triangle LNO and segment MP of triangle PNM. Hector wrote the following proof for his geometry homework for the given problem. Statements Reasons segment LN is congruent to segment NP Given ∠1 ≅ ∠2 Given Reflexive Property ΔLNO ≅ ΔPNM Angle-Angle-Side Postulate ∠NLO ≅ ∠NPM Corresponding Parts of Congruent Triangles Are Congruent Which of the following completes Hector's proof?

Answer 1

Answers: LNM MLN reflexive property ASA

It is given that angle LNO is congruent to angle LNM and angle OLN is congruent to angle MLN. We know that side LN is congruent to side LN because of the Reflexive Property. Therefore, because of ASA , we can state that triangle LNO is congruent to triangle LNM.

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Answer 2

I have seen Your question before many times:

If segment LN is congruent to segment NP and ∠1 ≅ ∠2, prove that ∠NLO ≅ ∠NPM:

Overlapping triangles LNO and PNM. The triangles intersect at point Q on segment LO of triangle LNO and segment MP of triangle PNM.

Hector wrote the following proof for his geometry homework for the given problem:

Statements Reasons
segment LN is congruent to segment NP Given
∠1 ≅ ∠2 Given
∠N ≅ ∠N Reflexive Property
ΔLNO ≅ ΔPNM Angle-Angle-Side Postulate
∠NLO ≅ ∠NPM

Which of the following completes Hector's proof?
Angle Addition Postulate
Converse of Corresponding Angles Postulate
Corresponding Parts of Congruent Triangles Are Congruent
Triangle Proportionality Theorem
______________________________
The answer:
The missing reason to complete Hector's proof is
Corresponding Parts of Congruent Triangles Are Congruent
It's been established in the previous statement that triangle LNO and triangle PNM are congruent by the AAS Postulate.
The proof:
Corresponding Parts of Congruent Triangles Are Congruent
is comprehensive.



Hope I helped!!!