Similarity Summary


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  • Enlargement or Dilatation
  • If DPQR is the image of DABC (Pre image) and K is the enlargement factor,
  • If K = 1 the triangles are congruent.
  • The ratio of their areas is K2
  • (SAS similarity)

If a pair of corresponding angles are equal and the sides including them are proportional, the triangles are similar.

  • (AA similarity)

If two pairs of corresponding angles are equal then the triangles are similar

  • (SSS similarity)

If three pairs of corresponding sides are proportional, then the two triangles are similar.

  • A perpendicular drawn from the right angle vertex of a right triangle to the hypotenuse divides the triangle into two triangles similar to each other and also to the original triangle.
  • In DABC,  if ÐA = 90o and AD ^ BC (D is the foot of the altitude)

AB2 = BC . BD, AC2 = BC . CD and AD2 = BD.CD



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