Question

determine whether the conditions ∠q≅∠n, ∠p≅∠m, and (overline{pq}congoverline{mn}) are sufficient to prove that (\triangle pqrcong\triangle mno) and justify your answer. are the conditions ∠q≅∠n, ∠p≅∠m, and (overline{pq}congoverline{mn}) sufficient to prove that (\triangle pqrcong\triangle mno)? no yes

Explanation:

Step1: Recall triangle - congruence criteria

The main triangle - congruence criteria are SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles).

Step2: Analyze given conditions

We are given two angles $\angle Q\cong\angle N$, $\angle P\cong\angle M$ and one side $\overline{PQ}\cong\overline{MN}$. This is the ASA (Angle - Side - Angle) congruence criterion. When two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent.

Answer:

Yes