Prove that the diagonals of a trapezium divide each other proportionally.

Consider the following statements : 1. The diagonals of a trapezium divide each other proportionally. 2. Any line drawn parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally. Which of the above statements is/are correct?

If the diagonals of a quadrilateral divide each other proportionally,prove that it is a trapezium

If the diagonals of a quadrilateral divide each other proportionally; then it is a trapezium.

If the diagonals of a quadirlateral divide each other proportionally then it is a

Prove that the diagonals of a rectangle bisect each other and are equal.

The diagonals of a parallelogram bisect each other.

The diagonals of a parallelogram bisect each other.

The diagonals of a |gm bisect each other

Prove that the line segment joining the mid- points of the diagonals of a trapezium is parallel to each of the parallel sides and is equal to half the difference of these sides.

Prove by vector method that the diagonals of a parallelogram bisect each other.