Question

In △LMN and △PQR, LM = PQ and MN = QR. What additional information is sufficient to conclude that △LMN ≅ △PQR?

A) ∠L = ∠P
B) ∠M = ∠Q
C) ∠N = ∠R
D) LM = MN = QR = PQ

Answer 1

To conclude that △LMN is congruent to △PQR given LM = PQ and MN = QR, the sufficient additional information is that ∠L = ∠P (∠M = ∠Q or ∠N = ∠R would also be sufficient). This satisfies the SAS Postulate for triangle congruence.

Step-by-step explanation:

In the case of triangles △LMN and △PQR, where LM = PQ and MN = QR, the additional information sufficient to conclude that △LMN ≅ △PQR is that one pair of corresponding angles is equal. This principle is derived from the SAS (Side-Angle-Side) Postulate, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Therefore, the answer is A) ∠L = ∠P. If ∠L is equal to ∠P, and we know that LM = PQ and MN = QR, then by the SAS Postulate, △LMN is congruent to △PQR.

Answer 2

The additional information that is sufficient to conclude that △LMN ≅ △PQR is ∠L = ∠P.

Step-by-step explanation:

The additional information that is sufficient to conclude that △LMN ≅ △PQR is option A) ∠L = ∠P. If we have the information that ∠L = ∠P, then we can conclude that the two triangles are congruent using the Angle-Angle-Side (AAS) congruence criterion.

According to AAS, if two angles of one triangle are congruent to two angles of another triangle, and the included sides are also congruent, then the triangles are congruent.