At a Glance - Proving Congruence
When two triangles are congruent, they're identical in every single way. Sure, they might be flipped or turned on their side or a million miles away, but they're still clones of each other. If two triangles are congruent, then we should be able to perform only congruence transformations in order to map one triangle onto the other.
That's all good and fine, but it doesn't help us when we're given side lengths and angle measures. What helps is knowing that when triangles are congruent, all their angles and sides are congruent too. Because we know that's true, we can say that corresponding parts of congruent triangles are congruent. We shorten this to CPCTC, just for fun. Kind of like the definition of what congruent triangles actually are.
Do we really have to check all of the edges and the angles to prove congruence? That is a lot of stuff to check, and we all have lives. Even the triangles have places to go and people to see. Isn't there a faster way?
We're glad we asked! (We wouldn't have had to ask if you'd just done it.) Yes, there is a better way. Actually, there are four better ways.