Question

What additional information could be used to prove that the triangles are congruent using AAS? Check all that apply.

C ≅ Q
CB ≅ QM
AC = 3.9cm and RQ = 3.9cm
mC = 35° and mQ = 35°
AB = 2.5cm and MQ = 2.5cm

Answer 1

The additional information could be used to prove that the triangles are congurent by AAS congurency property .

AC = 3.9cm and RQ = 3.9cm

and CB ≅ QM

Reason

In ΔABC and ΔQMR

(1) ∠ M = ∠ B= 29 °

(2)∠ R = ∠ A = 116 °

(3) AC = 3.9cm and RQ = 3.9cm

Thus angles are congurent by the AAS congurence property.

Thus AC = 3.9cm and RQ = 3.9cm are used to prove that the triangles are congurent .

Also in

In ΔABC and ΔQMR

(1) ∠ M = ∠ B= 29 °

(2)∠ R = ∠ A = 116 °

(3) CB ≅ QM

(Corresponding sides of the triangle as shown in the diagram)

Thus angles are congurent by the AAS congurence property.

Thus are CB ≅ QM used to prove that the triangles are congurent .

Hence proved

Answer 2

(B) and (C)

Explanation:

Consider ΔABC and ΔRMQ, we have

∠A=∠R=29° (Given)

∠B=∠M=116°(Given)

AC = 3.9cm and RQ = 3.9cm

Thus, by AAS rule of congruency, ΔABC ≅ ΔRMQ

therefore, the missing information is AC = 3.9cm and RQ = 3.9cm

Also, from ΔABC and ΔRMQ, we haqve

∠A=∠R=29° (Given)

∠B=∠M=116°(Given)

CB ≅ QM

Thus, by AAS rule of congruency, ΔABC ≅ ΔRMQ

therefore, the missing information is CB ≅ QM.

Hence, option B and C are correct.