To prove congruence between two triangles, we have to have enough information so that the size and shape are fixed. The size is determined by the length of a triangle's sides. The shape is determined by the angles.

All sides are known

When all sides of a triangle are known, we do not need to know any of the angles to prove congruence. There is only one triangle that can be drawn from three set sides. This is called the Side-Side-Side Congruence Theorem.

Two sides are known

When we know two sides, you need to know the angle that's in between the known sides, the included angle, to prove congruence. This is called the Side-Angle-Side Congruence Theorem.

One side is known

When you know only one side, you would need to know at least two angles to prove congruence with either the Angle-Angle-Side Congruence Theorem or the Angle-Side-Angle Congruence Theorem.

No sides are know

When no sides are known, it's impossible to prove congruence even if we know all of the angles. This makes the shape the same but the sizes of the triangles could be different.

Exercise