Final answer:
To prove Δmnq≅Δpoq, specific information about the triangles' sides and angles is needed to determine which congruence criterion applies: SSS, SAS, ASA, or AAS.
Step-by-step explanation:
To determine which triangle congruence criteria proves that Δmnq≅Δpoq, we would need specific information about the sides and angles of the triangles in question. The congruence criteria include:
- SSS (Side-Side-Side): This criterion states that if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.
- SAS (Side-Angle-Side): This criterion 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.
- ASA (Angle-Side-Angle): This criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
- AAS (Angle-Angle-Side): This criterion states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
Without additional specific information about triangles Δmnq and Δpoq, we cannot conclusively determine which criterion applies. In general, it is important to identify whether you are given information about sides or angles to apply the appropriate congruence criterion.