Two triangles are said to be congruent when the corresponding angles and the corresponding sides in both the triangles are same. i.e. both the triangles look like same, but one will be the mirror image of the other.
Here, ΔPQR and ΔLMN are congruent. Because
∠P is congruent to ∠L.
∠Q is congruent to ∠M.
∠R is congruent to ∠N.
PQ is congruent to LM.
QR is congruent to MN.
RP is congruent to NL.
But some times, we may not know all the 3 sides and 3 angles to determine whether the two triangles are congruent. In that case also, it is possible to determine the same just with 3 (instead of all 6) using the following 5 ways.
a) SSS:
SSS stands for Side, Side, Side. It means that, if 3 sides of a triangle are equal to the 3 sides of the other triangle then both triangles are congruent to each other.
b) SAS:
SAS stands for Side, Angle, Side. It means that, if 2 sides and included angle of a triangle are equal to the 2 sides and included angle of the other triangle then both triangles are congruent to each other.
c) ASA:
ASA stands for Angle, Side,Angle. It means that, if 2 angles and included side of a triangle are equal to the 2 angles and included side of the other triangle then both triangles are congruent to each other.
d) AAS:
AAS stands for Angle, Angle, Side. It means that, if 2 angles and non-included side of a triangle are equal to the 2 angles and non-included side of the other triangle then both triangles are congruent to each other.
e) HL :
This property is related to right angled triangle. HL stands for Hypotenuse, Leg. It means that, if the hypotenuse and leg of a right angled triangle are equal to the hypotenuse and leg of another right angled triangle both triangles are congruent to each other.
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