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Similar Figures


The rectilinear figures which have the same shape (resemble each other) but are not necessarily of the same size, are called similar figures.  Two rectilinear figures are said to be similar, if

(i) they are equiangular (i.e. corresponding angels are equal)

(ii) their corresponding sides are proportional.


For similarity both the conditions are necessary. 
For example a square and a rectangle are equiangular but they are not similar.




Similarly, a square and a rhombus have their corresponding sides proportional but they are
not similar.
2. The symbol ~ stands for ‘is similar to’.


Similar Triangles

 Similar Triangles: Two triangles are said to be similar if


(i)   they are equiangular and

(ii)  their corresponding sides are proportional

If two angles of one triangle are equal to two angles of another triangle, then the two triangles will be similar.

If in two triangles, one pair of corresponding sides are proportional and angles included by these sides are equal then the two triangles will be similar.

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