Two triangles are congruent if one can be placed exactly on top of the other, matching perfectly in every side length and every angle, through some combination of sliding, rotating and flipping. Checking congruence by comparing all three sides and all three angles individually works, but it's more measurement than actually necessary; a handful of shortcut rules let you prove two triangles are congruent from just a few carefully chosen matching measurements, without ever having to check the rest.
A triangle's shape and size are more tightly constrained than they first appear
A triangle turns out to be a surprisingly rigid shape: once you fix its three side lengths, there's only one possible triangle those lengths can form, up to moving, rotating or flipping it, which is exactly the insight behind the side-side-side congruence rule. Similarly, fixing two sides and the angle trapped between them, or two angles and the side between them, also pins down a triangle's shape and size completely, which gives the side-angle-side and angle-side-angle rules their power: each one identifies the smallest set of matching measurements that's actually enough to force two triangles into being identical.
Not every combination of three matching measurements actually guarantees congruence
These shortcut rules work precisely because of where the matching measurements sit relative to each other, and that detail matters more than it first seems: two sides and a non-included angle, an angle not trapped directly between the two known sides, can genuinely correspond to two different, non-congruent triangles, which is exactly why "angle-side-side" isn't a valid congruence rule even though it involves the same three types of measurement as the valid ones. Getting the shortcut rules right, and knowing which combinations don't actually guarantee congruence, is a large part of what geometric proof involving triangles is actually testing.
What we're still unsure about
That a specific, well-defined set of congruence rules, side-side-side, side-angle-side, angle-side-angle and their close relatives, correctly and completely determine triangle congruence is well established, rigorously proven geometry going back over two thousand years. What's more genuinely a matter of pedagogical approach is exactly how to teach students to reliably distinguish a valid congruence rule from an invalid-looking near-miss like angle-side-side, since that distinction depends on genuinely careful attention to which measurements are adjacent versus which are opposite, and maths educators continue to use different teaching strategies, worked counterexamples, physical manipulation, formal proof, to help that distinction actually stick rather than one method being clearly established as most effective.
This sits inside Triangles & Congruence, one of eight topics in Geometry, one of seven domains in Mathematics, one of seventeen subjects the app can quiz you on.