Question

what additional information could be used to prove △abc≅△mqr using sas? choose two correct answers. m∠a = 64° and ab = mq = 31 cm cb = mq = 29 cm ab = qr = 31 cm m∠q = 56° and cb≅rq m∠r = 60° and ab≅mq

Explanation:

Step1: Recall SAS criterion

SAS (Side - Angle - Side) requires two pairs of corresponding sides to be congruent and the included angles to be congruent.

Step2: Analyze each option

• For the first option: $m\angle A = 64^{\circ}$ and $AB = MQ=31$ cm. We need the included angles and corresponding sides. Here we don't know if the angles are included and correct corresponding sides.
• Second option: $CB = MQ = 29$ cm. If we consider the sides around the known angles in the two triangles, this gives us one pair of corresponding sides.
• Third option: $AB = QR = 31$ cm. This is not the correct corresponding side for SAS as we need the sides around the known angles.
• Fourth option: $m\angle Q = 56^{\circ}$ and $\overline{CB}\cong\overline{RQ}$. We don't have the correct side - angle - side combination.
• Fifth option: If $m\angle R = 60^{\circ}$ and $\overline{AB}\cong\overline{MQ}$, we have two pairs of corresponding sides ($\overline{AB}\cong\overline{MQ}$) and the included angles ($\angle C = 60^{\circ}$ and $\angle R=60^{\circ}$) which can be used for SAS. Also, $CB = MQ = 29$ cm gives a side and if we can match the included - angle situation, it can be used for SAS.

Answer:

B. $CB = MQ = 29$ cm, E. $m\angle R = 60^{\circ}$ and $\overline{AB}\cong\overline{MQ}$