In general, we come across several objects which have something common between them.  Observing them closely, we can see that some of them have same shape but may have different or same size such figures are called similar figures.
In case of triangles “Two triangles are said to be similar if their corresponding angles are equal and corresponding sides are proportional”.  By using AAA similarity theorem, SSS similarity theorem and SAS similarity theorem we can prove two triangles are similar.

AAA similarity theorem or criterion: If the corresponding angles of two triangles are equal, then their corresponding sides are proportional and the triangles are similar.

In DABC and DPQR, ,  and  then  and DABC ∼ DPQR
SSS similarity theorem or criteria: If sides of one triangle are proportional to the sides of the other triangles, then their corresponding angles are equal and the triangles are similar.
In DABC and DDEF,    then,  and  and DABC ∼ DDEF

SSS similarity theorem or criteria




SAS similarity theorem or criteria: If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the triangles are similar.
In DABC and DDEF,    and then  DABC ∼ DDEF

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