All rigid motions are transformations. Is the converse of this statement true. Explain your position. If you
believe it is false, provide a counter example (name a transformation that is not a rigid motion).

 

The statement "all rigid motions are transformations" is true.

Rigid motions include rotations, reflections, and translations (shifts).

The converse of a statement is basically switching the order, so the converse of "all rigid motions are transformations" would be:

"all transformations are rigid motions" (the converse)

This statement is NOT true

A counter example would be a dilation

Rigid motions preserve the size of the figure. All side lengths remain the same. However, a dilation changes the size of the shape or function. Since a dilation is a type of transformation that is not a rigid motion, the converse statement is false