Congruent triangles mean those triangles which are congruent with each other. Two triangles are said to be congruent if any of the following axioms are fulfilled: - SSS (Side, Side, Side) axiom, ASA (Angle, Side, Angle) axiom, SAS (Side, Angle, Side) axiom, AAS (Angle, Angle, Side) axiom and RHS (Right angle, Hypotenuse, Side) axiom. These five axioms are important for the proof of congruency.
This can be more clarified by the following examples:-
Example 1:- Proof that two triangles ABC and FDE shown below are congruent to each other.
All dimensions are in cm
Solution: In triangle ABC, AB = 50 cm, AC = 40 cm and BC = 60 cm
Now in triangle FDE, FD = 50 cm, FE = 40 cm and DE = 60 cm
By comparing both triangles we find the following:-
AB = FD = 50 cm,
AC = FE = 40 cm and
BC = DE = 60 cm
Therefore by SSS axiom,
Triangle ABC and Triangle FDE are congruent to each other
Example 2:- Proof that two triangles ABC and DEF shown below are congruent to each other.
Here AB = 10 cm and BC = 5 cm and angle ABC = 60 degree
Also DE = 10 cm and EF = 5 cm and angle DEF = 60 degree
In triangle ABC, AB = 10 cm, Angle ABC = 60 degree, BC = 5 cm
In triangle DEF, DE = 10 cm, Angle DEF = 60 degree and EF = 5 cm
By carefully examining we see the following:-
AB = DE,
Angle ABC = Angle DEF and
BC = EF
Therefore by axiom SAS, both triangles are congruent.