Two solids are similar if one is an enlargement, a reduction or a reproduction of the other.

### Properties

- All cubes are similar solids.
- All spheres are similar solids.
- The corresponding lengths in similar solids are proportional.

### Example

The dimensions of prism A are : *a*, *b* and *c.*

The dimensions of a similar prism B are : *ka*, *kb* and *kc.*

The ratio of similarity is *k* :

- If \(k=1\), then the two solids are congruent; one is a reproduction of the other.
- If \(0< k< 1\), then prism B is a reduction of prism A;
- If \(k> 1\), then prism B is an enlargement of prism A.

The volume of solid B is equal to the volume of solid A multiplied by the cube of the ratio of similarity *k*.

The area of solid B is equal to the area of solid A multiplied by the square of the ratio of similarity *k*.