Question

Why is the image of a figure after a translation is congruent to its preimage

Answer 1

"Translation" means "move it to a different place".

When you buy a hula-hoop or a frisbee and take it home from the store,
its shape doesn't change.  And when you leave home in the morning and
move yourself to school, your shape and size don't change.

Translation does not change the shape or the size of a figure.  All of its
sides and angles are still the same as they were in the original location.
Wherever it may go, it's still congruent to the picture of it that you took
before it moved.