Two figures are homothetic if they are related by an expansion or geometric contraction. 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.
Homothetic
See also
Directly Similar, Expansion, Geometric Contraction, Homothecy, Homothetic Center, Inversely Similar, Pantograph, Perspective, Similar, Similitude RatioExplore with Wolfram|Alpha
References
Casey, J. A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Dublin: Hodges, Figgis, & Co., p. 173, 1888.Durell, C. V. Modern Geometry: The Straight Line and Circle. London: Macmillan, pp. 1-2, 1928.Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, 1929.Lachlan, R. An Elementary Treatise on Modern Pure Geometry. London: Macmillian, p. 129, 1893.Referenced on Wolfram|Alpha
HomotheticCite this as:
Weisstein, Eric W. "Homothetic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Homothetic.html