Two or more figures are congruent if there is a rigid transformation that maps one figure onto the other. Figures are congruent if and only if they have the same side lengths and angle measures. For segments and angles alone, the definition still applies, congruent segments and angles have the same measures.

The symbol used to denote congruency is ≅, for example, △ABC ≅ △DEF. When you make a congruency statement, make sure the vertices of the figures are in the same location after the rigid transformation.

In the image to the right, △ABC maps on to △DEF by being reflected over line GH. Saying that △ACB ≅ △DEF is not a valid statement because after the reflection, point C maps to point F and not E.

If two figures are congruent, corresponding sides are also congruent (sides that are mapped to each other) and also corresponding angles are also congruent. In other words, congruent parts of congruent figures are congruent. (CPCFC)