The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry.


Home Analytic Geometry Triangle Congruent and Similar Triangles
See also: Congruence Transformation, Relations between Angles and Sides in Triangles 

Congruent and Similar Triangles

Congruent Triangles

For congruent triangles there are special rules. Two triangles are congruent if

  • the three sides are equal, or
  • two sides and the common angle are equal, or
  • two sides and the angle opposite the longer side are equal, or
  • one side and two angles are equal.
Please note that triangles with three equal angles are not necessarily congruent (since the sum of angles is always 180°, regardless of the length of the sides).

 

Similar Triangles

Two triangles are said to be similar if

  • the angles of each triangle are equal, or
  • the ratio between the three sides are equal, or
  • one angle and the ratio between two sides is equal.

Last Update: 2007-Sep-03