Let me start from the meaning of the term polygon.A polygon is a simple closed curve made up of three or more line segments.
Now coming to the meaning of term Rigid transformation ,It is either rotation,either Reflection,or Translation or combination of all these three.
The length of the sides of any polygon will not change i.e after rigid transformation shape and size of an object does not change.
So yes if two polygons are congruent ,they can always be mapped onto one through a series of rigid transformation i. Reflection,Rotation, or translation or combination of these.
Reflection takes place through a line.While Rotation means rotating a polygon through any angle, and translation means changing the coordinates of the polygon i.e certain integral value. You can Rotate the shape by any angle,and while translating you have to change the coordinate of each vertices by the same integral value.
In Reflection distance of the image from the line above or below is same.In rotation if you are rotating a polygon by an angle 0f 30° or 60° or 180°,the shape and size does not change but you are just rotating the shape. And in transformation you just take the shape or polygon by changing certain distance or when we consider two dimensional plane then by changing its coordinates without changing its shape and size.
