Question

what additional information could be used to prove that the triangles are congruent using aas or asa? select three options. ∠b≅∠p and bc≅pq ∠a≅∠t and ac = tq = 3.2cm ∠a≅∠t and ∠b≅∠p ∠a≅∠t and bc≅pq ac = tq = 3.2 cm and cb = qp = 2.2 cm

Explanation:

Step1: Recall AAS and ASA criteria

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

Step2: Analyze each option

• For $\angle B\cong\angle P$ and $\overline{BC}\cong\overline{PQ}$, we don't have enough information about angles and sides in the right combination for AAS or ASA.
• For $\angle A\cong\angle T$ and $AC = TQ=3.2$cm, if we consider the angles and the side, if we assume one more pair of angles are equal, it can be AAS or ASA.
• For $\angle A\cong\angle T$ and $\angle B\cong\angle P$, if we have a side congruent (either included or non - included), it can be AAS or ASA.
• For $\angle A\cong\angle T$ and $\overline{BC}\cong\overline{PQ}$, with $\angle A\cong\angle T$, if we consider non - included side and another angle, it can be AAS.
• For $AC = TQ = 3.2$cm and $CB=QP = 2.2$cm, this is SSS (Side - Side - Side) information, not relevant for AAS or ASA.

Answer:

$\angle A\cong\angle T$ and $AC = TQ = 3.2$cm, $\angle A\cong\angle T$ and $\angle B\cong\angle P$, $\angle A\cong\angle T$ and $\overline{BC}\cong\overline{PQ}$