Congruent Triangles

Definition of Congruent Triangles

Two triangles are said to be congruent if their corresponding sides and angles are equal.

More About Congruent Triangles

  • The following congruency tests are used to check the congruency of two triangles:
  • SAS Congruency Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
  • SSS Congruency Postulate: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
  • ASA Congruency Postulate: If two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle, then the two triangles are congruent.
  • SAA Congruency Postulate: If two angles and the non-included side of one triangle is congruent to two angles and the non-included side of another triangle, then the two triangles are congruent.

Video Examples: Introduction to Congruent Triangles


Example of Congruent Triangles

      example of Congruent_Triangles
  • Since all the sides and angles of the triangles ABC and MPN are equal, so triangle ABC is congruent to triangle MPN.

Solved Example on Congruent Triangles

Ques: ?ABC and ?EDF are congruent triangles. Find the length of EF.
    example of Congruent_Triangles

    Choices:
    A. 3 in.
    B. 4 in.
    C. 6 in.
    D. 5 in.
    Correct Answer: B

Solution:

    Step 1: Congruent triangles have congruent corresponding parts (sides and angles).
    Step 2: Length of EF = length of AC = 4 in.