A composition of two isometries results in the preservation of the length. From theorem 1241 of the composition of transformations, a composition of two isometries would be an isometry. An isometry is a transformation that is linear wherein the length is being preserved, there would be no change in the shape or size of a given figure. This includes translation, rotation, glides, identity map and reflection. When two figures are related by an isometry, they are said to be congruent. Another term for isometry is rigid transformation. Every isometry should have at least one point that is fixed. If a given isometry has more than one point that is fixed, it can be a transformation or a reflection.
