Two geometrical objects are called similar if they both have the same shape

Shape

The shape of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material...

. More precisely, either one is congruent

Congruence (geometry)

In geometry, two figures are congruent if they have the same shape and size. This means that either object can be repositioned so as to coincide precisely with the other object...

 to the result of a uniform scaling

Scaling (geometry)

In Euclidean geometry, uniform scaling is a linear transformation that enlarges or shrinks objects by a scale factor that is the same in all directions. The result of uniform scaling is similar to the original...

 (enlarging or shrinking) of the other. This means that either object can be rescaled and repositioned so as to coincide precisely with the other object.

Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure.