Question

which statements are true about additional information for proving that the triangles are congruent? select two options. if ∠a ≅ ∠t, then the triangles would be congruent by asa. if ∠b ≅ ∠p, then the triangles would be congruent by aas. if all the angles are acute, then the triangles would be congruent. if ∠c and ∠q are right angles, then triangles would be congruent. if (overline{bc}congoverline{pq}), then the triangles would be congruent by asa.

Explanation:

• For the first option: If \(\angle A\cong\angle T\), we have two angles (\(\angle A\) and the given equal angles in the triangles) and the included side (the side marked equal) which is not the case for ASA.
• For the second option: If \(\angle B\cong\angle P\), we have two angles (\(\angle B\) and \(\angle P\)) and a non - included side (the side marked equal) which satisfies AAS (Angle - Angle - Side) congruence criterion.
• For the third option: Just knowing all angles are acute does not provide any information about the sides or specific angle - side relationships for congruence.
• For the fourth option: If \(\angle C\) and \(\angle Q\) are right angles, we still need more information about sides or other angles to prove congruence.
• For the fifth option: If \(\overline{BC}\cong\overline{PQ}\), we have two angles (the given equal angles) and the included side (\(\overline{BC}\) and \(\overline{PQ}\)) which satisfies ASA (Angle - Side - Angle) congruence criterion.

Answer:

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