Class 03 Geometry Congruency of triangles By Er. V.K Roy

In geometry, congruence of triangles refers to the condition where two triangles are identical in size and shape. This means that their corresponding sides and angles are equal. When two triangles are congruent, one triangle can be placed exactly over the other, and they will coincide completely.
The symbol for congruence is '≅', so if two triangles △ABC\triangle ABC△ABC and △DEF\triangle DEF△DEF are congruent, we write:
△ABC≅△DEF\triangle ABC \cong \triangle DEF△ABC≅△DEF
There are several criteria (rules) used to determine the congruence of triangles:


SSS (Side-Side-Side) Congruence Criterion: If the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.


SAS (Side-Angle-Side) Congruence Criterion: If two sides and the angle between them in one triangle are respectively equal to the corresponding two sides and the included angle of another triangle, the triangles are congruent.


ASA (Angle-Side-Angle) Congruence Criterion: If two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, the triangles are congruent.


RHS (Right angle-Hypotenuse-Side) Congruence Criterion: If in two right-angled triangles, the hypotenuse and one corresponding side are equal, the triangles are congruent.


AAS (Angle-Angle-Side) Congruence Criterion: If two angles and one non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent.


Key Points:


Congruent triangles have identical corresponding sides and angles.


The congruence criteria are used to prove that two triangles are congruent.


Congruent triangles are essential in proving various geometric theorems.
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