The phenomenon says that if two figures are of the same shape and size or they can be termed as the mirror image of each other; then the two given figures are said to be congruent to each other. For the study of polygons, mainly triangles, congruence is a very important concept to know. For 2 polygons to be congruent, they must have an equal number of sides. So there are some rules by which we can determine if two triangles are said to be congruent or not.
S (Side) - S (Side) - S (Side) Rule: This rule says that 2 triangles are said to be congruent if all the sides of the 2 triangles are equivalent. S (Side) - A (Angle) - S (Side) Rule: 2 triangles are said to be congruent if one interior angle and 2 sides of a triangle are equivalent to the interior angle and 2 sides of the other triangle. The angle should be held between the two equivalent sides.
A (Angle) – S (Side) - A (Angle) Rule: If 2 angles and the included side of a triangle are equivalent to the corresponding side included between the 2 angles in the other triangle, then the triangles are said to be congruent. R (Right-Angle) – H (Hypotenuse) – S (Side): If in a right-angled triangle, the hypotenuse and any one of the sides are equivalent to the corresponding hypotenuse and the side of the triangle, then those 2 triangles are said to be a congruent triangle.
The chapter also discusses the congruence of line segments and angles. A very commonly used symbol for congruence is ≅ in the world of mathematics. The chapter also teaches the students about the various relations and properties in a congruent figure.