Question

congruence: asa and aas
what additional information could be used to prove that the triangles are congruent using aas? choose two correct answers.

ab = 2.5 cm and mq = 2.5 cm
∠c ≅ ∠q
m∠c = 35° and m∠q = 35°
overline{cb} ≅ overline{qm}
ac = 3.9 cm and rq = 3.9 cm

Explanation:

Step1: Recall AAS congruence

AAS (Angle - Angle - Side) congruence 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.

Step2: Analyze each option

• Option 1: \(AB = 2.5\space cm\) and \(MQ = 2.5\space cm\)

There is no information about the relationship of these sides with the angles in the triangles for AAS.

• Option 2: \(\angle C\cong\angle Q\)

We already have \(\angle A=\angle R = 29^{\circ}\) and \(\angle B=\angle M=116^{\circ}\). If \(\angle C\cong\angle Q\), but we still need a side. This alone is not sufficient for AAS.

• Option 3: \(m\angle C = 35^{\circ}\) and \(m\angle Q = 35^{\circ}\)

Since \(\angle A=\angle R = 29^{\circ}\) and \(\angle B=\angle M = 116^{\circ}\), and if \(\angle C=\angle Q = 35^{\circ}\), we still need a non - included side. This alone is not sufficient for AAS.

• Option 4: \(\overline{CB}\cong\overline{QM}\)

We have \(\angle A=\angle R\) and \(\angle B=\angle M\). If \(\overline{CB}\cong\overline{QM}\) (a non - included side), then by AAS \(\triangle ABC\cong\triangle RMQ\).

• Option 5: \(AC = 3.9\space cm\) and \(RQ = 3.9\space cm\)

We have \(\angle A=\angle R\) and \(\angle B=\angle M\). If \(AC = RQ\) (a non - included side), then by AAS \(\triangle ABC\cong\triangle RMQ\).

Answer:

\(\overline{CB}\cong\overline{QM}\), \(AC = 3.9\space cm\) and \(RQ = 3.9\space cm\)