Frequently we compare both figures on a plane and solids. When comparing the measurement of their sides and angles, there is a possibility of similarity or congruence (isometry).
Similarity is the property that describes if a group of figures or solids are related by a scale factor. In other words, the measurements of the corresponding angles are equal, while the measurements of the corresponding sides are proportional.
If the figures or solids are identical in all respects, we say they are congruent or isometric.
Two figures or solids are said to be congruent if one can be geometrically transformed into the other through the application of an isometry or a series of isometries. An isometry is a transformation, such as a rotation, translation or reflection, that does not change the size, shape, or angles of a figure. Two congruent figures or solids have equal side lengths and equal angle measurements.
Finally, we can also notice that there is a relationship between the areas of two figures or the volumes of two solids.
Figures are equivalent if and only if they have the same area.
Solids are equivalent if and only if they have the same volume.
Note: Equivalent figures or equivalent solids can be completely different shapes. For example, a prism with a pentagonal base can be equivalent to a pyramid with a rectangular base.