Congruence

Concept of Congruence
In our daily life, we observe the shaving blades of different brands always fit into a safety-razor. Why? All the blades are identical as they have exactly the same size and shape. Other examples are a pattern repeated in a printed fabric, two key of the same lock, any original part of a machine, and its replacement are some of the examples of things having exactly the same size and shapes.

Geometrical figures which have exactly the same size and shape are called Congruent. If two figures have the same shape but not the size then they are called Similar.

CONGRUENT TRIANGLES
If two triangles are equal in all respects, they are said to be congruent. Thus two congruent triangles have the same shape and the same size.
Note 1: Congruent triangles coincide by superposition.
Congruent triangles are similar but the converse is not always true.
The symbol ≡ reads “is congruent to”
Case 1 (SAS Congruence Condition):
If two sides and the included angle of one triangle are equal to two sides and the included angle of the other, then the triangle is congruent.

Case 2(SSS Congruence Condition):
If the three sides of one triangle are equal to the three sides of the other, then the triangles are congruent.

Case 3(ASA Congruence Condition):
If two angles and the included side of the one are respected equally to the two angles and the included side of the other.

Case 4(RHS Congruence Condition):
If two right-angled triangles have their hypotenuses and one side equal then the triangles are congruent.