Question

which triangle congruence postulate or theorem can be used to prove $\triangle lmn \cong \triangle pqr$? images of triangles lmn and pqr with markings a) asa b) sas c) aas d) not enough information

Explanation:

Step1: Identify Marked Parts

In $\triangle LMN$ and $\triangle PQR$:

• One side in $\triangle LMN$ (e.g., $MN$) and one side in $\triangle PQR$ (e.g., $QR$) are marked with one tick (so $MN = QR$).
• One side in $\triangle LMN$ (e.g., $LM$) and one side in $\triangle PQR$ (e.g., $PR$) are marked with two ticks (so $LM = PR$).
• The included angles: $\angle N$ in $\triangle LMN$ and $\angle R$ in $\triangle PQR$ are marked as equal.

Step2: Match with Congruence Postulate

The SAS (Side - Angle - Side) postulate states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent. Here, we have two sides (one - ticked and two - ticked) and the included angle (between the two sides) equal in both triangles. So the SAS postulate applies.

Answer:

B. SAS