when two figures or objects in geometry have the same shape and size, or if one has the same shape and size as the mirror image of the other From Wikipedia, the free encyclopedia
In geometry, two figures or objects and are congruent (written as )[1] if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.[2]
More formally, two sets of points are called congruent, if and only if one can be transformed into the other by isometry.[3] For isometry, rigid motions are used.
This means that two geometrical figures are congruent if one object can be repositioned, rotated or reflected—but not resized—so that it coincides exactly with the other object.[4] if one can be moved or rotated so that it fits exactly where the other one is, then the two figures are congruent. If one of the object has to change its size, then the two objects are not congruent: they are just called similar.
As an example, two distinct plane figures on a piece of paper are congruent if we can cut them out and then match them up completely (turning the paper over here is permitted).
Congruent polygons are polygons that if you fold a regular polygon in half that is a congruent polygon.[needs to be explained]
The following are a few rules to make new shapes congruent to the original one:
The relationship, that a shape is congruent to another shape, has three famous properties:
The famous three properties, reflexivity, symmetry and transitivity, together make the notion of equivalence. Hence, the property congruence is one sort of equivalence relation between shapes of a plane.
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