Two figures are homothetic if they are related by a Dilation (a dilation is also known as a Homothecy). This means that they lie in the same plane and corresponding sides are Parallel; such figures have connectors of corresponding points which are Concurrent at a point known as the Homothetic Center. The Homothetic Center divides each connector in the same ratio , known as the Similitude Ratio. For figures which are similar but do not have Parallel sides, a Similitude Center exists.
See also Dilation, Homothetic Center, Perspective, Similitude Ratio
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA:
Houghton Mifflin, 1929.