### 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 '$\cong$'.  If the object $$A$$ is congruent to object $$B$$, it can be denoted as $$A$$ $\cong$ $$B$$.
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: 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 $$AB$$$\cong$$$CD$$
Two angles have the same measure are called congruent angles, but they lie in different orientation or position.
Example: 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 $$∠R$$$\cong$$$∠Q$$
Two circles have the same size(radius, diameter or circumference) are called congruent circles, but they can overlap.
Example: 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 $$P$$ $\cong$ circle $$Q$$
Two polygons have an equal number of sides, and all the corresponding sides and angles are congruent are called congruent polygons.
Example: 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. $$ABCDE$$ $\cong$ $$PQRST$$.