Question

Construct a counterexample to show that AAA is not a criterion for congruent triangles.

Thank you in advance

Answer 1

The best example to show that AAA cannot be a congruence criterion is to choose a equilateral triangle. Any equilateral triangle has all the angles equal to 60 degrees, but side length may vary.

For e.g. An equilateral triangle of side length 4 units and another equilateral triangle of side length 1 unit, both have all angles equal but they will not be congruent. So AAA is not a congruence criterion.

We have an another counterexample shown below: