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:

• For AAS (Angle - Angle - Side) congruence, we need two angles and a non - included side.
• In \(\triangle ABC\) and \(\triangle RMQ\), we already know \(\angle A=\angle R = 29^{\circ}\) and \(\angle B=\angle M=116^{\circ}\).
• If \(\overline{CB}\cong\overline{QM}\), then by AAS, \(\triangle ABC\cong\triangle RMQ\) (the non - included side for the two known angles).
• If \(AC = RQ\) (i.e., \(AC = 3.9\mathrm{cm}\) and \(RQ = 3.9\mathrm{cm}\)), then by AAS, \(\triangle ABC\cong\triangle RMQ\) (the non - included side for the two known angles).

Answer:

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