Question

22092x0xry_cms 2025-2026 nc math 2 credit recovery
triangle 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
$ac = 3.9$ cm and $rq = 3.9$ cm
$overline{cb} \cong overline{qm}$
$m\angle c = 35^\circ$ and $m\angle q = 35^\circ$
$\angle c \cong \angle q$

Explanation:

Step1: Recall AAS congruence rule

AAS requires two pairs of congruent angles and one pair of non-included congruent sides.

Step2: Calculate third angle of triangles

For $\triangle ABC$: $m\angle C = 180^\circ - 29^\circ - 116^\circ = 35^\circ$
For $\triangle RMQ$: $m\angle Q = 180^\circ - 29^\circ - 116^\circ = 35^\circ$

Step3: Evaluate each option

• Option 1 ($AB=2.5$ cm, $MQ=2.5$ cm): $\angle A \cong \angle R$, $\angle B \cong \angle M$, non-included sides $AB \cong MQ$ → fits AAS.
• Option 2 ($AC=3.9$ cm, $RQ=3.9$ cm): $\angle A \cong \angle R$, $\angle C \cong \angle Q$, non-included sides $AC \cong RQ$ → fits AAS.
• Option 3 ($\overline{CB} \cong \overline{QM}$): These are included sides between the two known angles, which is ASA, not AAS.
• Option 4 ($m\angle C=35^\circ$, $m\angle Q=35^\circ$): Only confirms angle congruence, no side congruence provided.
• Option 5 ($\angle C \cong \angle Q$): Only confirms one more angle congruence, no side congruence provided.

Answer:

1. $AB = 2.5$ cm and $MQ = 2.5$ cm
2. $AC = 3.9$ cm and $RQ = 3.9$ cm