Congruence of Triangles
Congruent means coinciding exactly when superimposed. Two geometrical figures are said to be congruent if they have exactly the same shape and size and the property is called congruence.
Congruence of Two Line Segmentsb :
Two linesegments will be congruent if and only if their lengths are equal.
Congruence of Two Line Segments

Two linesegments PQ and AB are congruent if AB = PQ
Two triangles are congruent, if all the sides and all the angles of one are equal to the corresponding sides and angles of the other.
Congruence of Two Angles
When Î”ABC is congruent to Î”PQR we get six equalities; three of the corresponding sides and three of the corresponding angles. Suppose Î”ABC superimposes Î”PQR exactly and the vertices of Î”ABC fall on the vertices of Î”PQR in the order A â†” P, B â†” Q, C â†” R or we may write in short as ABC â†” PQR
Then we have the six equalities:
(i) AB = PQ
(ii) BC = QR
(iii) CA = RP
(iv) âˆ ABC = âˆ PQR or âˆ B = âˆ Q
(v) âˆ BCA = âˆ QRP or âˆ C = âˆ R
(vi) âˆ CAB = âˆ RPQ or âˆ A = âˆ P
In the two triangles ABC and PQR, there will be six matching or correspondence between their vertices:
A â†” P B â†” Q C â†” R or ABC â†” PQR
A â†” Q B â†” R C â†”P or ABC â†” QRP
A â†” R B â†” P C â†” Q or ABC â†” RPQ
A â†” P B â†” R C â†” Q or ABC â†” PRQ
A â†” Q B â†” P C â†” R or ABC â†” QPR
A â†” R B â†” Q C â†” P or ABC â†” RQP
If Î”ABC is congruent to Î”PQR, then one of the matching ones will superimpose exactly on the other. The corresponding side angles of the two triangles will be equal (congruent).
Two triangles are congruent if and only if there exists a correspondence between their vertices such that the corresponding sides and angles of the two triangles are equal.