What additional information could be used to prove ΔABC ≅ ΔMQR using SAS? Select two options.

Answer: 1) m∠A = 64° and AB = MQ = 31 cm

3) m∠Q = 56° and CB ≅ RQ

Step-by-step explanation:

By the SAS postulate of congruence, Two triangles are called congruent if any pair of corresponding sides and their included angles are congruent in both triangles.

1) If m∠A = 64° and AB = MQ = 31 cm is given,

Then we can write,

AB ≅ MQ

∠ A ≅ ∠ M

And, AC ≅ RM

Where AB, and AC are corresponding to MQ and RM respectively and Angle A and angle M are included angles in triangles ABC and MQR.

⇒ Δ ABC ≅ Δ MQR

2) If CB = MQ = 29 cm is given,

Then We have,

CB ≅ MQ

and AC ≅ RM

But the included angles ∠C and ∠M of these corresponding sides are not congruent.

⇒ By second option we can not prove, triangles ABC and MQR are congruent.

3) If m∠Q = 56° and CB ≅ RQ is given,

Then, We have,

m∠R = 60°

⇒ ∠C ≅ ∠R

Where CB, and AC are corresponding to RQ and RM respectively and Angle C and angle R are included angles in triangles ABC and MQR.

⇒ Δ ABC ≅ Δ MQR

4) If m∠R = 60° and AB ≅ MQ is given,

∠C ≅ ∠R

But, Angle C and R are not the included angle of congruent corresponding sides of triangles ABC and MQR.

⇒ we can not prove, triangles ABC and MQR are congruent.

5) If AB = QR = 31 cm is given,

Then there are not any pair of congruent angles in triangles ABC and MQR.

⇒ we can not prove triangle ABC and MQR are congruent.

Answer: A and C