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Triangles A B C and R M Q are shown. Angles C A B and M R Q are 29 degrees. Angles A B C and R M Q are 116 degrees.

What additional information could be used to prove that the triangles are congruent using AAS? Select two options.

AngleC ≅ AngleQ
CB ≅ QM
AC = 3.9cm and RQ = 3.9cm
mAngleC = 35° and mAngleQ = 35°
AB = 2.5cm and MQ = 2.5cm

1 answer

To prove that triangles ABC and RMQ are congruent using the Angle-Angle-Side (AAS) theorem, you need to show that two angles and a corresponding non-included side of one triangle are equal to the two angles and corresponding non-included side of the other triangle.

Given that angle CAB ≅ angle MRQ (both are 29 degrees) and angle ABC ≅ angle RMQ (both are 116 degrees), you already have two pairs of angles.

Now, you need to identify which additional pieces of information can help you with the congruency proof. You would need one of the side lengths that corresponds to the angles.

Among the options provided, the ones that would help in establishing the AAS congruence are:

  1. AB = 2.5cm and MQ = 2.5cm (provides a corresponding side length)
  2. AC = 3.9cm and RQ = 3.9cm (also provides a corresponding side length)

Therefore, the best options to use to prove that triangles ABC and RMQ are congruent using AAS are:

  • AB = 2.5cm and MQ = 2.5cm
  • AC = 3.9cm and RQ = 3.9cm