Similar figures have equal corresponding angles and all corresponding distances in the same positive ratio, called the ratio of magnification (Coxeter and Greitzer 1967, p. 94). A transformation that takes figures to similar figures is called a similarity.

Two similar figures are directly similar when all corresponding angles are equal and described in the same rotational sense. This relationship is written . (The symbol is also used to mean "is the same order of magnitude as" and "is asymptotic to.") Two similar figures are inversely similar when all corresponding angles are equal and described in the opposite rotational sense.

See also

Coincident, Congruent, Directly Similar, Homothetic, Inversely Similar, Napoleon's Theorem, Similar Matrices, Similar Polygons, Similar Triangles, Similarity, Spiral Similarity Explore this topic in the MathWorld classroom

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References

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., 1967.Durell, C. V. "Similar Figures." Ch. 1 in Modern Geometry: The Straight Line and Circle. London, England: Macmillan, pp. 1-9, 1928.Kern, W. F. and Bland, J. R. "Similar Figures." §22 in Solid Mensuration with Proofs, 2nd ed. New York: Wiley, pp. 4 and 53-57, 1948.Lachlan, R. "The Theory of Similar Figures." Ch. 9 in An Elementary Treatise on Modern Pure Geometry. London, England: Macmillian, pp. 128-147, 1893.Neuberg and Tarry. Mathesis 2.Project Mathematics. "Similarity." Videotape. http://www.projectmathematics.com/similar.htm.

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Weisstein, Eric W. "Similar." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Similar.html

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