When proving that a quadrilateral is a parallelogram by using slopes you must find

By using vectors prove that a quadrilateral is a parallelogram if and only if the diagonals bisect each other.

ABCD is a quadrilateral and BD is one of its diagonals, as shown in the figure. Prove that quadrilateral ABCD is a parallelogram, also find its area.

When proving that quadrilateral is a trapezium it is neccesary to show ____.

Prove that the lines joining the midpoints of consecutive sides of a quadrilateral form a parallelogram using vector method.

Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other.(a) If you live in Delhi, then you have winter clothes. (i) If you do not have winter clothes, then you do not live in Delhi. (ii) If you have winter clothes, then you live in Delhi.(b) If a quadrilateral is a parallelogram, then its diagonals bisect each other. (i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. (ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.