Which transformation will always map a parallelogram onto itself?

a 90° rotation about its center

a reflection across one of its diagonals

a 180° rotation about its center

a reflection across a line joining the midpoints of opposite sides

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

is only a line? i think so