18.19 In the quadrilateral formed by connecting the midpoints of the sides of the following quadrilaterals, which one is centrally symmetric but not axially symmetric?
(A) A quadrilateral with perpendicular diagonals.
(B) A quadrilateral with equal diagonals.
(C) A quadrilateral with perpendicular and equal diagonals.
(D) A quadrilateral with neither perpendicular nor equal diagonals.
(5th "Jinyun Cup" Junior High School Mathematics Invitational, 1988)
[Solution] The line segments connecting the midpoints of the sides of any quadrilateral form a parallelogram. A general parallelogram is a centrally symmetric figure.

If the diagonals of the original quadrilateral are perpendicular to each other, then the midpoint quadrilateral is a rectangle, which is an axially symmetric figure, so (A) is not true.

If the diagonals of the original quadrilateral are equal, then the midpoint quadrilateral is a rhombus, which is also an axially symmetric figure, so (B) is not true.
Therefore, (C) is not true.
Hence, the answer is (D).