Question

which statements are true about additional information for proving that the triangles are congruent? choose two correct answers. if ∠c and ∠q are right angles, then triangles would be congruent. if ∠b ≅ ∠p, then the triangles would be congruent by aas. if bc̅ ≅ pq̅, then the triangles would be congruent by asa. if all the angles are acute, then the triangles would be congruent.

Explanation:

Step1: Analyze congruence criteria

Triangle congruence requires SSS, SAS, ASA, AAS, or HL. AAA (all angles) only ensures similarity.

Step2: Evaluate each option

• "All acute angles": AAA, not congruent. Incorrect.
• "∠C and ∠Q right angles": Only right angles insufficient. Incorrect.
• "BC ≅ PQ by ASA": If ∠C=∠Q (right angles), BC=PQ (included side), and another angle congruent, ASA applies. Correct.
• "∠B ≅ ∠P by AAS": With ∠C=∠Q (right angles), ∠B=∠P, and a non-included congruent side (e.g., AC=QT from hash mark), AAS applies. Correct.

Answer:

If $\overline{BC} \cong \overline{PQ}$, then the triangles would be congruent by ASA., If $\angle B \cong \angle P$, then the triangles would be congruent by AAS.