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:

Step1: Recall congruence postulates

ASA (Angle - Side - Angle) requires two angles and the included side to be congruent. AAS (Angle - Angle - Side) requires two angles and a non - included side to be congruent.

Step2: Analyze each option

• If $\angle A\cong\angle T$, we have two angles ($\angle A\cong\angle T$ and the given equal angles at $C$ and $Q$) and the included side between them is not given as congruent, so it's not ASA. This is false.
• If $\angle B\cong\angle P$, along with the given equal angles at $C$ and $Q$ and the non - included side (the side opposite the given equal angles), the triangles would be congruent by AAS. This is true.
• Just because all angles are acute does not prove triangle congruence. This is false.
• Just because $\angle C$ and $\angle Q$ are right angles does not prove triangle congruence without more information. This is false.
• If $\overline{BC}\cong\overline{PQ}$, along with the given equal angles at $C$ and $Q$ and the other given equal angles, the triangles would be congruent by ASA. This is true.

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.