Given a triangle ABC which is isosceles but not equilateral. That is, AB = AC, but AB does not equal BC. How many congruences are there, between triangle ABC and itself? Here's my answer: By the hypothesis, we can infer that triangle ABC is congruent to triangle ACB. So there is just one congruence. My professor said that there is another congruence but I just can't figure out what it is. Can someone please help me? Would it be that triangle ABC is congruent to triangle ACB which is congruent to triangle BAC? Thank you!