Question

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

Explanation:

Step1: Recall AAS and ASA congruence rules

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

Step2: Analyze Option 1

For $\angle B\cong\angle P$ and $\overline{BC}\cong\overline{PQ}$, we don't have enough angle - angle information for AAS or ASA, so this is incorrect.

Step3: Analyze Option 2

For $\angle A\cong\angle T$ and $AC = TQ=3.2$ cm. If we consider AAS, we need another angle. For ASA, the side is not between the angles, so this is incorrect.

Step4: Analyze Option 3

For $\angle A\cong\angle T$ and $\angle B\cong\angle P$, if we consider two angles of one triangle are congruent to two angles of another triangle, this can be used for AAS (if we can show a non - included side congruent) or ASA (if we can show the included side congruent). This is a valid option.

Step5: Analyze Option 4

For $\angle A\cong\angle T$ and $\overline{BC}\cong\overline{PQ}$, with two angles and a non - included side, this can be used for AAS. This is a valid option.

Step6: Analyze Option 5

For $AC = TQ = 3.2$ cm and $CB=QP = 2.2$ cm, this is SSS (Side - Side - Side) information, not AAS or ASA, so this is incorrect.

Answer:

$\angle A\cong\angle T$ and $\angle B\cong\angle P$, $\angle A\cong\angle T$ and $\overline{BC}\cong\overline{PQ}$