Question

what additional information could be used to prove that the triangles are congruent using aas? select two options.
□∠c≅∠q
□cb≅qm
□ac = 3.5cm and rq = 3.5cm
□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 the corresponding two angles and non - included side of another triangle, the triangles are congruent.

Step2: Analyze the given angles

We already have one pair of angles equal (the given non - marked angles in each triangle which are equal as they are vertical angles). We need another pair of angles and a non - included side.

Step3: Check each option

• $\angle C\cong\angle Q$ gives us another pair of angles.
• $\overline{CB}\cong\overline{QM}$ gives us a non - included side.
• $AC = 3.5\text{cm}$ and $PQ=3.5\text{cm}$ is a non - included side.
• $m\angle C = 35^{\circ}$ and $m\angle Q = 35^{\circ}$ gives us another pair of angles.
• $AB = 2.5\text{cm}$ and $MQ = 2.5\text{cm}$ is not a non - included side for the known angles.

The pairs that work for AAS are:

• Option 1: $\angle C\cong\angle Q$ (provides the second pair of angles)
• Option 2: $\overline{CB}\cong\overline{QM}$ (provides the non - included side)

Answer:

$\angle C\cong\angle Q$, $\overline{CB}\cong\overline{QM}$