An example of congruence. The two triangles on the left are congruent, while the third is similar to them. The last triangle is neither similar nor congruent to any of the others. Note that congruence permits alteration of some properties, such as location and orientation, but leaves others unchanged, like distance and angles. The unchanged properties are called invariants.

In geometry, two figures or objects \displaystyle{ F } and \displaystyle{ F' } are congruent (written as \displaystyle{ F \cong F' }) if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

More formally, two sets of points are called congruent, if and only if one can be transformed into the other by isometry. For isometry, rigid motions are used.