TOPICS

# Similar

Two figures are said to be similar when all corresponding angles are equal and all distances are increased (or decreased) in the same 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 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 figures are inversely similar when all corresponding angles are equal and described in the opposite rotational sense.

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

## Explore with Wolfram|Alpha

More things to try:

## 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: 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: Macmillian, pp. 128-147, 1893.Neuberg and Tarry. Mathesis 2.Project Mathematics. "Similarity." Videotape. http://www.projectmathematics.com/similar.htm.

Similar

## Cite this as:

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