Question

what additional information could be used to prove that the triangles are congruent using aas? select two options.
□∠c≅∠q
□cb≅qm
□ac = 3.9cm and rq = 3.9cm
□m∠c = 35° and m∠q = 35°
□ab = 2.5cm and mq = 2.5cm

Explanation:

Step1: Recall AAS congruence criterion

AAS (Angle - Angle - Side) states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent. In \(\triangle ABC\) and \(\triangle RMQ\), we already know that \(\angle A=\angle R = 29^{\circ}\) and \(\angle B=\angle M=116^{\circ}\).

Step2: Analyze each option

• Option 1: \(\angle C\cong\angle Q\) only gives another angle equality, but we need a non - included side for AAS. So this is not correct.
• Option 2: \(\overline{CB}\cong\overline{QM}\) is a non - included side with respect to the known angles. This can be used for AAS.
• Option 3: \(AC = 3.9\text{cm}\) and \(RQ = 3.9\text{cm}\), \(AC\) and \(RQ\) are not non - included sides with respect to the known angles \(\angle A,\angle B\) and \(\angle R,\angle M\). So this is not correct.
• Option 4: \(m\angle C = 35^{\circ}\) and \(m\angle Q = 35^{\circ}\) gives another angle equality, not a non - included side for AAS. So this is not correct.
• Option 5: \(AB = 2.5\text{cm}\) and \(MQ = 2.5\text{cm}\), \(AB\) and \(MQ\) are non - included sides with respect to the known angles \(\angle A,\angle B\) and \(\angle R,\angle M\). This can be used for AAS.

Answer:

B. \(\overline{CB}\cong\overline{QM}\), E. \(AB = 2.5\text{cm}\) and \(MQ = 2.5\text{cm}\)