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 for two triangles to be congruent.

Step2: Analyze option 1

For $\angle B\cong\angle P$ and $\overline{BC}\cong\overline{PQ}$, we don't have enough information about the third - angle or side relationship for AAS or ASA.

Step3: Analyze option 2

If $\angle A\cong\angle T$ and $AC = TQ=3.2$ cm, if we consider the non - included side and one angle, this can be used for AAS if we have another angle congruent.

Step4: Analyze option 3

If $\angle A\cong\angle T$ and $\angle B\cong\angle P$, we can use AAS if we have a side congruent. But this alone is not enough for ASA or AAS without a side.

Step5: Analyze option 4

If $\angle A\cong\angle T$ and $\overline{BC}\cong\overline{PQ}$, this can be used for AAS as we have two angles and a non - included side.

Step6: Analyze option 5

If $AC = TQ = 3.2$ cm and $CB=QP = 2.2$ cm, this is SSS (Side - Side - Side) criterion, not AAS or ASA.

Answer:

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