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: Analyze the ASA (Angle - Side - Angle) congruence condition

ASA requires two angles and the included side to be congruent. For the first option, if \(\angle A\cong\angle T\), we don't have the included side information. For the fifth option, if \(\overline{BC}\cong\overline{PQ}\), we don't have the two - angle information for ASA.

Step2: Analyze the AAS (Angle - Angle - Side) congruence condition

AAS requires two angles and a non - included side to be congruent. In the second option, if \(\angle B\cong\angle P\), we already have \(\angle C\cong\angle Q\) (from the given angle markings) and a non - included side (the side opposite to the angles).

Step3: Analyze the right - angle case

If \(\angle C\) and \(\angle Q\) are right angles (fourth option), we can use AAS (since we have two angles: the right angles and the other given equal angles, and a non - included side).

Step4: Analyze the "all angles are acute" case

Just knowing that all angles are acute is not a valid congruence criterion. Congruence criteria are SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA, AAS, and HL (Hypotenuse - Leg for right - angled triangles).

Answer:

If \(\angle B\cong\angle P\), then the triangles would be congruent by AAS; If \(\angle C\) and \(\angle Q\) are right angles, then triangles would be congruent.