1) AAA or AA 2) SSS 3) SAS.

If in two triangles, (i)the corresponding angles are equal, then their corresponding sides are proportional (i.e. in the same ratio) and hence the triangles are similar.

In two triangles ABC and DEF are similar,if

(i) ∠A = ∠D, ∠B = ∠E, ∠C = ∠F and

$\frac{AB}{DE}=\frac{BC}{EF}=\frac{CA}{FD}$

In such a case, we write ΔABC ~ ΔDEF

ΔXYZ ~ ΔLMN by SSS criteria.

Two triangles XYZ and LMN such that

$\frac{XY}{LM}=\frac{YZ}{MN}=\frac{XZ}{LN}$ Then the two triangles are similar by SSS similarity.

In triangle ABC and DEF, ∠A = ∠D

$\frac{AB}{DE}=\frac{AC}{DF}$

Then the two triangles ABC and DEF are similar by SAS.

• AAA Similarity

• AA Similarity

• SSS Similarity

• SAS Similarity

• Practice on Similarity

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