In triangles, there are three criteria that can be used to prove two triangles are congruent, namely: Sides (SSS): If three sides of one triangle are equal in length to three sides of another triangle, then the two triangles are congruent. Angles (SSS): If three angles in one triangle are equal to three angles in another triangle, then the two triangles are congruent. Angles-side-angles (SAS): If two angles and one side of one triangle are equal to two angles and one side of another triangle, then the two triangles are congruent. Based on the parallelogram above, it can be seen that triangles ABC and ACD have sides AC the same length and angles ADC and BCA the same size. Therefore, we can use the SAS criterion to prove that the two triangles are congruent. Here is the way: We know that side AC in triangle ABC is the same length as side AC in triangle ACD. We also know that angle ADC in triangle ACD is equal to angle BCA in triangle ABC. We can conclude that side AD in triangle ACD is the same length as side BC in triangle ABC, because the SAS criterion requires the presence of one side that is the same length and two angles that are the same measure. We can also conclude that the angle ACD in triangle ACD is equal to angle CAB in triangle ABC, because the two angles are opposite angles on the line AC. We can conclude that triangles ABC and triangle ACD are congruent based on the SAS criteria. So, the correct answer is C. Angles-side-angles (SAS).