There are 3 main criteria for similarity of triangles

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

(ii)

AB BC CA ---- = ------ = ------ DE EF FD |

In such a case, we write ΔABC ~ ΔDEF

ΔXYZ ~ ΔLMN by SSS criteria.

Two triangles XYZ and LMN such that

XY YZ XZ ---- = ------ = ------ LM MN LN |

In triangle ABC and DEF,

∠A = ∠D and | AB BC CA ---- = ------ = ------ DE EF FD |

• AAA Similarity

• AA Similarity

• SSS Similarity

• SAS Similarity

• Practice on Similarity

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