Question

what additional information could be used to prove that the triangles are congruent using aas? select two options.

∠c ≅ ∠q

overline{cb} ≅ overline{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 (Angle - Angle - Side) congruence criterion

AAS 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 triangles are congruent.

Step2: Analyze each option

• Option 1: \(\angle C\cong\angle Q\)

This is just an angle - angle (AA) condition without the side. So, it is not sufficient for AAS.

• Option 2: \(\overline{CB}\cong\overline{QM}\)

In \(\triangle ABC\) and \(\triangle RMQ\), \(\angle A = 29^{\circ}\), \(\angle B=116^{\circ}\), \(\angle R = 29^{\circ}\), \(\angle M = 116^{\circ}\). If \(\overline{CB}\cong\overline{QM}\), then we have two angles (\(\angle A\cong\angle R\), \(\angle B\cong\angle M\)) and a non - included side (\(\overline{CB}\cong\overline{QM}\)) which satisfies AAS.

• Option 3: \(AC = 3.9\mathrm{cm}\) and \(RQ = 3.9\mathrm{cm}\)

Since \(AC\) is a side in \(\triangle ABC\) and \(RQ\) is a side in \(\triangle RMQ\), and \(\angle A\cong\angle R\), \(\angle B\cong\angle M\), \(AC\) and \(RQ\) are non - included sides. So, this satisfies AAS.

• Option 4: \(m\angle C = 35^{\circ}\) and \(m\angle Q = 35^{\circ}\)

This is just an angle - angle (AA) condition without the side. So, it is not sufficient for AAS.

• Option 5: \(AB = 2.5\mathrm{cm}\) and \(MQ = 2.5\mathrm{cm}\)

\(AB\) is included between \(\angle A\) and \(\angle B\) in \(\triangle ABC\), and \(MQ\) is included between \(\angle M\) and \(\angle Q\) in \(\triangle RMQ\). So, it does not satisfy AAS.

Answer:

B. \(\overline{CB}\cong\overline{QM}\), C. \(AC = 3.9\mathrm{cm}\) and \(RQ = 3.9\mathrm{cm}\)