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Chapter - 16

Similarity-

Two figures are said to be similar if they have the same shape but different size.

In the above diagram, ABC, A’B’C’, A’’B’’C’’ and A'’’B’'’C’'’ are similar.

Two triangles are said to be similar if the angles of one triangle are equal to the corresponding angles of the other and their corresponding sides are proportional.

Two triangles are said to be equiangular if the angles of one are equal to the corresponding angles of another.

If two angles of one triangle are equal to the two angles of another triangle, the third angle will be automatically equal and the triangles will be equiangular.

In the above diagram, are similar if

Note : - Congruent triangles are always similar but converse is not true.

Similarity Criterian

1. SAS – Criteria : - If two triangles have a pair of equal angles and the sides containing these equal angles are proportional, then the triangles are similar.

In the abvoe diagram, if

then are similar.

2. AAA or AA Criteria : - If two triangles have two pairs of corresponding angles equal the triangles are similar.

then are similar.

3. SSS – Criteria : - If sides of two triangles are proportional, the triangles are similar:

In the above diagram, if