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
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
Angle-Angle-Side Postulate
∠ NLO ≅ ∠ NPM Corresponding Parts of Congruent Triangles Are Congruent
Which of the following completes Hector's proof? (6 points)
ΔLNO ≅ ΔPNM
ΔLNO ≅ ΔMQL
ΔMQL ≅ ΔOQP
ΔOQP ≅ ΔPNM
To complete Hector's proof, we need to provide a valid reasoning that justifies the congruence of ∠ NLO and ∠ NPM. In this case, we can use the Angle-Angle-Side (AAS) postulate.
Here's the completed proof:
Statements Reasons
segment LN is congruent to segment NP Given
∠ 1 ≅ ∠ 2 Given
∠ N ≅ ∠ N Reflexive Property
∠ LNO ≅ ∠ NPM Angle-Angle-Side Postulate (∠ 1 ≅ ∠ 2, segment LN ≅ segment NP)
∠ NLO ≅ ∠ NPM Corresponding Parts of Congruent Triangles Are Congruent
Therefore, the correct completion for Hector's proof is:
ΔLNO ≅ ΔPNM