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
∠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

Answer 1

Angle-Angle-Side Postulate

Explanation:

Answer 2

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.