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**CONDITIONS OF CONGRUENCY OF TRIANGLES**

Two triangles can be proved congruent using any of the following criteria :

** I. SSS Congruency Criterion (Side-Side-Side) **

If three sides of a triangle are equal to the corresponding sides of another triangle, then the two triangles are congruent by SSS congruence criterion.

In *∆*ABC and *∆*PQR

AB = PQ = 3 cm

BC = QR = 4 cm

AC = PR = 2 cm

**II. SAS Congruency Criterion (Side-Angle-Side)**

If two triangles have two corresponding sides equal and the angle included between these sides is also equal, then the two triangles are congruent by SAS congruence criterion.

**Note: ** Two triangles need not be congruent if the length of two sides and a non included angle (i.e. angle is not between the two given sides) of one triangle are equal to the length of two sides & a non-included angle of the other triangle

** III. ASA Congruency Criterion (Angle-Side-Angle)**

If two angles and the included side of one triangle are equal to the two corresponding angles and included side of another triangle, then the two triangles are congruent by ASA congruence criterion.

**IV. AAS Congruency Criterion (Angle-Angle-Side)**

If two angles and side opposite to one of the angles of one triangle are equal to two corresponding angles and side opposite to one of angles, then the two triangles are congruent by AAS congruence criterion.

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