what additional information could be used to prove $\triangle abccong\triangle mqr$ using sas? select two…
what additional information could be used to prove $\triangle abccong\triangle mqr$ using sas? select two options. $mangle a = 64^{circ}$ and $ab = mq = 31$ cm $cb = mq = 29$ cm $mangle q = 56^{circ}$ and $overline{cb}congoverline{rq}$ $mangle r = 60^{circ}$ and $overline{ab}congoverline{mq}$ $ab = qr = 31$ cm
Answer
Explanation:
Step1: Recall SAS (Side - Angle - Side) criterion
SAS requires two pairs of corresponding sides to be congruent and the included angles to be congruent.
Step2: Analyze each option
- For option 1: $m\angle A = 64^{\circ}$ and $AB = MQ=31$ cm. We have one side and one non - included angle, not enough for SAS.
- For option 2: $CB = MQ = 29$ cm gives only one side, not enough for SAS.
- For option 3: $m\angle Q=56^{\circ}$ and $\overline{CB}\cong\overline{RQ}$ gives one side and one non - included angle, not enough for SAS.
- For option 4: If $m\angle R = 60^{\circ}$ and $\overline{AB}\cong\overline{MQ}$, in $\triangle ABC$ and $\triangle MQR$, we have $\angle C=60^{\circ},\angle R = 60^{\circ}$, $AB = MQ$ and the sides that include the angles ($AC$ and $MR$ are not given yet, but we have the correct angle - side combination for SAS).
- For option 5: $AB = QR=31$ cm gives only one side, not enough for SAS.
Answer:
$m\angle R = 60^{\circ}$ and $\overline{AB}\cong\overline{MQ}$