Similarity

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Study the following figures. They have the same shape though their sizes are different. One figure is the enlargement of the other figure.

These figures are said to be similar to each other. In our study, we mostly deal with similarity of triangles.

Two triangles are similar if

(i) Their angles are the same and

(ii) The corresponding sides are proportional

(i) ÐA = ÐX, ÐB = ÐY and ÐC = ÐZ

(ii)

The symbol for similarity is '~',

For the above case,

DABC is similar to DXYZ.

(i) If two triangles are congruent, then they are similar. Its converse is not true.

(ii) = a constant.

Let the constant be equal to K. Then K is called enlargement factor (or the dilation factor/scale factor/magnification factor). AB is K times XY and so on.