Similarity of Triangles

Any two polygons, with corresponding angles equal and corresponding sides proportional, are similar. Thus, two polygons are similar, if they satisfy the following two conditions:

  1. Corresponding angles are equal.
  2. The corresponding sides are proportional.

Even if one of the conditions does not hold, the polygons are not similar.

Similarity of Triangles

Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional.

When ΔABC is similar to ΔDEF, it is written as

ΔABC ~ ΔDEF

∠A = ∠D, ∠B = ∠E, ∠C = ∠F

AB/DE = BC/EF = CA/FD

AAA Criterion for Similarity

If in two triangles, the corresponding angles are equal the triangles are similar.

SSS Criterion for Similarity

If the corresponding sides of two triangles are proportional the triangles are similar.

SAS Criterion for Similarity

If one angle of a triangle is equal to one angle of the other triangle and the sides containing these angles are proportional, the triangles are similar.