Congruence of triangles

Aug 09, 2022, 16:45 IST

About congruence of triangles

In a pair of triangles if all three corresponding sides and three corresponding angles are exactly equal, then the triangles are said to be congruent

Two triangles are congruent, if there exists a correspondence between their vertices such that the corresponding sides and the corresponding angles of the two Ds are equal or congruent.

CONGRUENCE RELATION

(i)    Every triangle is congruent to itself i.e. 

►ABC = ►ABC

(ii)   If ►ABC = ►DEF

            then ►DEF = ►ABC

(iii)         If ►DEF = ►ABC, and

                then ►DEF = ►PQR then

               ►ABC = ►PQR

Criteria for Congruency

Following are the criteria for the congruency of the triangles

Side-angle-side (SAS) congruence criterion

Two triangles are congruent if two sides and therefore the included angle of 1 triangle are adequate to the corresponding sides and therefore the included angle of the opposite triangle

Find below pdf of solved example of congruence of triangles