Two polygons are congruent if and only if there exists a composition of __ that maps one polygon to the other polygon.

two polygons are congruent if and only if there exists a composition of translation/rotations that maps one polygon to the other polygon.

(instead of translations/rotations we could write transformations, but there are transformations that also change the size of the figure, so I think that writing translations/rotations is more precise)

Step-by-step explanation:

Two figures are congruent if they have the same shape and size.

So for example, if we have one triangle, and we reflect that triangle along some line, those bot images will have the same shape and size (but maybe different orientations) so the triangles are still congruent.

Also, we could translate the image, or simply rotate it along some point, and the resulting image will be congruent to the initial image.

Then two polygons are congruent if and only if there exists a composition of translation/rotations that maps one polygon to the other polygon.

step-by-step explanation:

a and d