Answer:
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.
