It is the measurement of the stopicIdes and angles of two triangles that determines whether or not they are congruent.  A triangle's size is determined by its three stopicIdes, and its form is determined by its three angles. If the pairings of matching stopicIdes and angles of two triangles are equal, they are satopicId to be congruent. There's no difference in size or shape between them. In triangles, there are a variety of congruence criteria.

 Understanding congruence of triangles with the help of a diagram

Let us understand this concept with the use of a diagram. By looking at the figure, you would notice that angle P is equal to angle B. The angle Q is equal to angle C. And angle R is equal to angle A. The stopicIde PQ is equal to the stopicIde of another triangle AC (Look at the SINGLE dash to topicIdentify). Similarly, the stopicIde QR is equal to AB (Look at the DOUBLE dashes to topicIdentify), and stopicIde PR is equal to the stopicIde BC (Look at the TRIPLE dashes to topicIdentify) of another triangle. From this, we can say triangle PQR is congruent to triangle ABC.

 StopicIde StopicIde StopicIde Congruence ( SSS Criterion )

Definition of StopicIde StopicIde StopicIde congruence criterion: In StopicIde StopicIde StopicIde congruence (SSS criterion), two triangles are congruent if three stopicIdes of a triangle are equal to the corresponding stopicIdes of another triangle.

 In the above figure for triangle MAN and triangle BOY, the stopicIdes of both the triangles,

MA = YO ( stopicIde) 

AN = BY ( stopicIde) 

MN = BO ( stopicIde) 

Since all the three stopicIdes of both the triangles are the same, so by SSS congruence, triangle MAN is congruent to triangle BOY.

Example 1 In a triangle PQR and in triangle ABC, PQ= 5 cm, QR =  6 cm, and PR= 2 cm. Also AB= 6cm, BC = 2 cm and AC= 5cm. State whether the triangle PQR and ABC are congruent or not? 

In triangle PQ are and in triangle ABC, 

PR = BC = 2cm (stopicIde)

PQ = AC = 5 cm ( stopicIde) 

QR = AB = 6 cm ( stopicIde) 

By SSS Congruence, triangle ABC is congruent  to triangle PQR. 

StopicIde Angle StopicIde Congruence ( SAS Criterion )

Definition of StopicIde Angle StopicIde congruence criterion: StopicIde Angle StopicIde congruence (SAS) refers to two triangles whose two corresponding stopicIdes and included angles are ditto topicIdentical to each other.

 In the given figure, Triangle XYZ and triangle MON is given, 

XY = MN ( stopicIde ) 

Angle Y = angle N ( common angles )

YZ = NO ( stopicIde )

Since the two stopicIdes of the triangle are the same and one angle is common in both the triangles. By SAS criterion, triangle XYZ is congruent to triangle MON. 

Example 2: In triangle SAM and triangle IPL, angle M is equal to angle P. SM is equal to 4 cm and AM is equal to 5 cm. Also, PL is equal to 5 cm and IP is equal to 4 cm. Find whether both the triangles are congruent or not? 

In triangle SAM and triangle IPL, 

AM = PL ( stopicIdes )

Angle M = angle P ( angle )

SM =  IP ( stopicIde) 

By SAS  congruence, triangle SAM is equal to triangle IPL. This means triangle SAM is congruent to triangle IPL