Geometry (please help, quick)

Question

If  and ∠ 1 ≅ ∠ 2, prove that ∠ NLO ≅ ∠ NPM:

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

StatementsReasons
	Given
∠ 1 ≅ ∠ 2	Given
∠ N ≅ ∠ N	Reflexive Property
ΔLNO ≅ ΔPNM
∠ NLO ≅ ∠ NPM	Corresponding Parts of Congruent Triangles Are Congruent

Which of the following completes Hector's proof?

Angle-Angle-Side Postulate

Angle-Side-Angle Postulate

Side-Angle-Side Postulate

Side-Side-Side Postulate

Answer 1

In this proof, you are given a common angle to both triangles (angle N), a pair of congruent long sides (NL & NP), and two other congruent angles (angle 1 & angle 2). This fits the criteria for AAS exactly. So that is the correct answer.

As a side note, if the question had been to prove angle NLO is congruent to angle NPM, you could actually reach that conclusion without ever having to say the triangles are congruent. Since angle N is common to both triangles and angle 1 is congruent to angle 2, that means that angle NLO must be congruent to angle NPM also, since the sum of the angles in a triangle must equal 180 degrees.

That's just an observation, though. The question specifically asks the reason why the two triangles are congruent, so AAS is the proper response in this case.

And by the way, I also agree that it should have been referred to as a theorem as opposed to a postulate. I guess that one slipped by the editors.

Answer 2

AAS...although I would NOT call it a postulate; it is a theorem proved from other theorems and postulates.

Remember AAS depends on the fact that the sum of the angles of a triangle is 180 degrees and then ASA is the theorem needed to complete that proof.