Congruent Triangles

Two triangles are congruent (written $\triangle ABC \cong \triangle DEF$) when they are identical in both shape and size — one is an exact copy of the other, perhaps flipped or turned. Their matching (corresponding) sides and angles are all equal.

You don't need to check all six measurements. Any one of these minimum conditions proves congruence:

• SSS — three pairs of sides equal.
• SAS — two sides and the included angle equal.
• ASA (or AAS) — two angles and a corresponding side equal.
• RHS — right angle, hypotenuse and one side equal (right-angled triangles only).

Corresponding parts then match up in the order the letters are written: in $\triangle ABC \cong \triangle DEF$, side $AB$ equals side $DE$.