Question

Determine whether angle-angle-angle (AAA) is a valid means for establishing triangle congruence. If it is a valid criterion, explain why. If it is not valid, use GeoGebra to create a counterexample demonstrating that it doesn’t work and give an explanation. If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the space below.

Answer 1

AAA is not a valid congruence theorem. This is because we can construct two different triangles, of different shapes, and they both have the same corresponding angles. See the diagram below. Simply form any triangle you want and scale up or down to form a second triangle. The two triangles are similar, but they aren't congruent. They need to be the same size and shape to be congruent.