Congruent
Elementary
Think of two shapes cut out of paper. The shapes are congruent if both shapes have the same form and the same size, so that one could be placed exactly on top of the other (possibly after flipping it over).
High school (geometry)
Consider two figures in the plane, and the rigid motions that move one of them: rotations, reflections, and translations. The figures are congruent if such motions can move one exactly onto the other: the figures have the same shape and the same size.
Examples
Examples
- $3$ and $10$, as integers modulo $7$ High school
- Two $3$-$4$-$5$ triangles in different places High school
Notes
In number theory, “congruent” has a different meaning: $a \equiv b \pmod{n}$ means $n$ divides $a - b$. Both meanings are equivalence relations.
Distinctions involving this term
- Types of sameness: Mathematics has many ways to say that two objects are “the same.” Equal objects are the same object. The other words describe objects that are different but “the same in some respect,” and each one depends on what respect is meant.