Congruent Triangles - Why AAA doesn't work

Having all three corresponding angles equal is not enough to prove congruence

Try this Drag any orange dot at P or R in the right-hand triangle. It will change size while keeping all three angles congruent to the left triangle.

Notice that as you drag the points P or R, the triangle grows and shrinks so as it keeps all three corresponding angles the same as the left triangle ABC. It is clear that the two triangles cannot be congruent because they can have different sizes.

What does this mean?

It means that just because two triangles have congruent corresponding angles, it does not prove the triangles are congruent.

But they are similar

Triangles like this that are the same shape but different sizes are called similar triangles. For more on this see Similar Triangles

Other congruence topics

Congruent Triangles

Congruent Polygons