section_path: Properties/Similarity and congruence
section_name: Similarity and congruence
paragraph_text: Similarity and congruence
  
  Two triangles are said to be similar, if every angle of one triangle has the same measure as the corresponding angle in the other triangle. The corresponding sides of similar triangles have lengths that are in the same proportion, and this property is also sufficient to establish similarity.
  
  Some basic theorems about similar triangles are:
  
  Two triangles that are congruent have exactly the same size and shape. All pairs of congruent triangles are also similar, but not all pairs of similar triangles are congruent. Given two congruent triangles, all pairs of corresponding interior angles are equal in measure, and all pairs of corresponding sides have the same length. This is a total of six equalities, but three are often sufficient to prove congruence.
  
  Some individually necessary and sufficient conditions for a pair of triangles to be congruent are: