Theory:

The congruent types are depending upon their shapes. They are as follows:
  • Congruence line segment
  • Congruence angles
  • Congruence circles
  • Congruence polygons
Important!
Notation for congruence relation is ''.  If the object \(A\) is congruent to object \(B\), it can be denoted as \(A\)  \(B\).
Two line segments have the same length are called a congruent line segment, but they need not lie at the same angle or position on the plane.
Example:
Theory_2.1.png
In here, \(AB\) and \(CD\) are line segments in equal length.  As the two line segments \(AB\) and \(CD\) have the same length, they are congruent line segments. It can be written as \(AB\)\(CD\)
Two angles have the same measure are called congruent angles, but they lie in different orientation or position.
Example:
Theory_2.2.png
In here \(∠R\) measure \(x°\) and \(∠Q\) measure \(x°\).  So both measures same.  Thus, \(∠R\) and \(∠S\) are congruent angles.  It can be written as \(∠R\)\(∠Q\)
Two circles have the same size(radius, diameter or circumference) are called congruent circles, but they can overlap.
Example:
Theory_2.3.png
In here, circle \(P\) has the radius \(r\) units and the circle \(Q\) has the same radius\(r\) units.  So both have same size.  Thus, circle \(P\) and \(Q\) are congruent angles. circle \(P\)  circle \(Q\)
Two polygons have an equal number of sides, and all the corresponding sides and angles are congruent are called congruent polygons.
Example:
Theory_2.4.png
In here, the both polygons \(ABCDE\) and \(PQRST\) have \(5\) sides and \(AB = PQ\), \(BC = QR\), \(CD = RS\), \(DE = ST\) and \(EA = TP\).  Also, its angles measures \(∠A = ∠P\), \(∠B = ∠Q\), \(∠C = ∠R\), \(∠D = ∠S\) and \(∠E = ∠T\),  Thus, the polygons \(ABCDE\) and \(PQRST\) have equal number of sides and all the corresponding sides and angles are congruent.  So they are congruent polygon. \(ABCDE\)  \(PQRST\).