Question

1. in △mno and △pqr, ∠mno≅∠pqr and no≅qr. what additional congruence is needed to prove that △mno and △pqr are congruent by sas postulate? a. mo≅pr b. mn≅pq c. ∠mon≅∠prq d. ∠omn≅∠rpq

Explanation:

Step1: Recall SAS postulate

The Side - Angle - Side (SAS) postulate 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 two triangles are congruent.
We are given that $\angle MNO\cong\angle PQR$ and $\overline{NO}\cong\overline{QR}$. The included angles for the pairs of congruent sides need to be considered.

Step2: Analyze the options

For $\triangle MNO$ and $\triangle PQR$ to be congruent by SAS, we need the sides adjacent to the given congruent angles to be congruent and the included angles to be congruent. The sides adjacent to $\angle MNO$ and $\angle PQR$ are $\overline{MN}$ and $\overline{PQ}$ respectively. So we need $\overline{MN}\cong\overline{PQ}$.

Answer:

B. $\overline{MN}\cong\overline{PQ}$