Congruence in a math context usually refers to the congruence of lines, shapes/figures, and angles. For example, line segments with the same length are congruent, and angles with the same measure are congruent.
Congruent figures are figures that have the same size and shape. For example, in the figure below, there are three pairs of congruent figures: the pair of cubes, triangles, and lines.
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Identical twins have congruent, or almost congruent features.