△DEF is rotated about point N to △D′E′F′.
A rotation is a transformation that turns a figure about a fixed point called the center of rotation. In your case the center of rotation is point N. A rotation is an isometric transformation: the original figure and the image are congruent. Main properties of rotation:
1) A rotation preserves lengths of segments.
2) A rotation preserves degrees of angles.
3) A rotation maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.
Therefore, option C is true (because the original figure and the image are congruent) and option D is false (because the original figure and the image must be congruent).
All corresponding points on the image and pre-image are equidistant to point N. This option is true (because rotation preserves lengths of segments), thus, DN≅D'N'.
