Asked by ashley
Triangles A B C and M Q R are shown. The lengths of sides A C and R M are congruent. Angle A C B is 60 degrees and angle R M Q is 64 degrees. Triangle A B C is rotated 90 degrees up and to the left to form triangle M Q R.
What additional information could be used to prove ΔABC ≅ ΔMQR using SAS? Select two options.
m∠A = 64° and AB = MQ = 31 cm
CB = MQ = 29 cm
m∠Q = 56° and CB ≅ RQ
m∠R = 60° and AB ≅ MQ
AB = QR = 31 cm
All Answers 1
Answered by
GPT-5 mini
AI
Options 1 and 3.
- Option 1: m∠A = 64° and AB = MQ. Since m∠M = 64° (given) and AC = RM (given), we have AB = MQ, AC = RM and ∠A = ∠M, so ΔABC ≅ ΔMQR by SAS.
- Option 3: m∠Q = 56° and CB ≅ RQ. With m∠M = 64° (given) and m∠Q = 56°, m∠R = 180° − 64° − 56° = 60°, which equals ∠C (given). Together with AC = RM and CB = RQ, this gives AC = RM, CB = RQ and ∠C = ∠R, so ΔABC ≅ ΔMQR by SAS.
- Option 1: m∠A = 64° and AB = MQ. Since m∠M = 64° (given) and AC = RM (given), we have AB = MQ, AC = RM and ∠A = ∠M, so ΔABC ≅ ΔMQR by SAS.
- Option 3: m∠Q = 56° and CB ≅ RQ. With m∠M = 64° (given) and m∠Q = 56°, m∠R = 180° − 64° − 56° = 60°, which equals ∠C (given). Together with AC = RM and CB = RQ, this gives AC = RM, CB = RQ and ∠C = ∠R, so ΔABC ≅ ΔMQR by SAS.
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