Congruence is a the state of agreement. It meaning is taken from a Latin word congruō which means “I meet together, I agree”. There is a difference between congruence and similarity. Congruence, as opposed to approximation, is a relation which implies a species of equivalence.
Congruence DefinitionBack to Top
2) A statement that two numbers or geometric figures are congruent
In the above figure triangle ABC and triangle XYZ are congruence. The definition of congruence triangle is when two or more triangle have all three sides exactly same and all three angles are same.
Here side AB = side XY
side AC = side XZ
side CB = side ZY
Triangle CongruenceBack to Top
Congruence RelationBack to Top
Congruence TheoremsBack to Top
(1) SAS (side angle side)
(2) SSS (side side side)
(3) ASA (angle side angle)
(4) AAS (angle angle side)
(5) RHS or HL (right hypotenuse side)
(6) AAA (angle angle angle)
SSS Statement: Two triangles are congruent, if three sides of one triangle are equal to the corresponding three sides of the other triangle.
ASA Statement: If in two triangles, two angles and one side are equal then triangles are congruent.
RHS Statement: If hypotenuse of a right angle triangle is congruent to hypotenuse of another right angle triangle and leg (perpendicular) of one right angle triangle is congruent to leg of other right angle triangle then both triangle will be congruent to each other, this is called hypotenuse leg theorem.
Congruence SymbolBack to Top
Congruence and SimilarityBack to Top
Congruence: The shapes are Congruence, if one shape can become another using Turns, Flips and/or Slides.
Similarity: A similarity transforms a object into a similar object but the size may varies. The only difference between congruence and similarity is size variation. When two triangles are congruence the size will be same and in similarity size can be change.