2. WHAT IS CONGRUENCE ???
Two figures are said to be congruent if they have the same shape and size.
The symbol of congruence is ≅ and is read as ‘congruent to’.
3. CONGRUENCE RELATION
Every triangle is congruent to itself , example ABC ≅ ABC
If ABC ≅ PQR , then PQR ≅ ABC
If ABC ≅ PQR , and PQR ≅ DEF
, then ABC ≅ DEF ABC
PQR
ABC
PQR
DEF
4. CONGRUENCE OF TRIANGLES
Congruent triangles have the same size and shape . Two triangles are said to
be congruent if there exists one-to-one correspondence between their
vertices such that the angles and the corresponding sides of the two triangles
are equal.
Two triangles are said to be congruent if these four cases apply on them :-
1 if all the sides are equal (SSS)
2 if two sides and the included angle are equal (SAS)
3 if two angles and the included side are equal (ASA)
4 if one right angle , Hypotenuse and a side are equal (RHS)
5. CASE – 1 THE THREE SIDES
Two triangles are congruent if the three sides of one triangle are respectively
equal to the three sides of the other triangle.
Triangle ABC is congruent to PQR by SSS case.
6. CASE-2 TWO SIDES AND THE INCLUDED
ANGLE
Two angles are congruent if the two sides and the included angle of one
triangle are respectively equal to the two sides and the included angle of the
other angle.
Triangle ACB is congruent to RPQ by SAS case
7. CASE-3 TWO ANGLES AND THE INCLUDED
SIDE
Two triangles are congruent if the two angles and the included side of triangle
are respectively equal to the angles and the included side of the other
triangle.
Triangle RPQ is congruent to VST by ASA case.
8. CASE-4 RIGHT ANGLE, HYPOTENUSE AND
A SIDE
Two right triangles are congruent if the hypotenuse and one side of one
triangle are respectively equal to the hypotenuse and one side of the other
triangle.
Triangle ABC is congruent to PQR by RHS case.
