Difference between revisions of "Similarity (geometry)"
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Informally, two objects are '''similar''' if they are similar in every aspect except possibly size or orientation. For example, a globe and the surface of the earth are, in theory, similar. | Informally, two objects are '''similar''' if they are similar in every aspect except possibly size or orientation. For example, a globe and the surface of the earth are, in theory, similar. | ||
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| + | More formally, we say two objects are [[congruent (geometry)|congruent]] if they are the same up to translation, rotation and reflection ([[rigid motion]]s). We say two objects are similar if they are congruent up to a [[dilation]]. | ||
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| + | All circles are similar. Two [[triangle]]s are similar if they have the same [[angle]]s. Two [[polygon]]s are similar if their corresponding angles are equal and corresponding sides are in a fixed [[ratio]]. | ||
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== See also == | == See also == | ||
Revision as of 14:20, 19 August 2006
Informally, two objects are similar if they are similar in every aspect except possibly size or orientation. For example, a globe and the surface of the earth are, in theory, similar.
More formally, we say two objects are congruent if they are the same up to translation, rotation and reflection (rigid motions). We say two objects are similar if they are congruent up to a dilation.
All circles are similar. Two triangles are similar if they have the same angles. Two polygons are similar if their corresponding angles are equal and corresponding sides are in a fixed ratio.
See also
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