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.

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

ΔABC and ΔEDF are congruent triangles. Find the length of EF.

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.

Related Terms for Congruent Triangles

  • ASA Congruency Postulate
  • Congruent
  • SAA Congruency Postulate
  • SAS Congruency Postulate
  • SSS Congruency Postulate
  • Sides
  • Triangle