similarity in geometry
Two figures and in a Euclidean plane or space (http://planetmath.org/EuclideanVectorSpace) are similar iff there exists a bijection from the set of points of onto the set of points of such that, for any , the ratio
of the lengths of the line segments and is always the same number , where and .
The number is called the ratio of similarity or the line ratio of the figure with respect to the figure (N.B. the in which the figures are mentioned!). The similarity of and is often denoted by
The corresponding angles (consisting of corresponding points) of two similar figures are equal.
The lengths of any corresponding arcs of two similar figures are proportional in the ratio .
The areas of two similar regions are proportional in the ratio when is the line ratio of the regions.
The volumes of two similar solids are proportional in the ratio when is the line ratio of the solids.
|Title||similarity in geometry|
|Date of creation||2013-03-22 17:08:48|
|Last modified on||2013-03-22 17:08:48|
|Last modified by||pahio (2872)|
|Defines||ratio of similarity|