Answer: The congruent pair is 2 and 4.
Step-by-step explanation: We are given four pairs of polygons, and we are to select the one in which the two polygons are congruent.
We can see in the figure that the polygons in pairs 1 and 3 cannot be congruent as they have different shapes and sizes.
In figure 2, each polygon is comprised of one rectangle of length 6 units and breadth 2 units and one right-angled triangle with base 2 units and height 2 units.
Therefore, they are congruent and will have the same area which is equal to
[tex]A=6\times2+\dfrac{1}{2}\times2\times2=12+2=14~\textup{sq. units.}[/tex]
In figure 4, there are two right-angled triangles with same base of length 8 units and heights of both the triangles is 4 units.
Therefore, they are congruent and will have same area, which is equal to
[tex]\dfrac{1}{2}\times 8\times4=16~\textup{sq. units}.[/tex]
Thus, the polygons in pairs 2 and 4 are congruent to each other.
