What can be concluded about triangle ABC?

Question

What can be concluded about triangle ABC if it is given that (a) ∆ABC congruent ∆ACB? (b) ∆ABC congruent ∆BCA?

Answer 1

If ΔABC ≅ ΔACB, then ∠B ≅ ∠C. So ΔABC is isosceles. (Note the order of the letters)

If ΔABC ≅ ΔBCA, then ΔABC is equilateral.