The midpoint of two opposite sides of a quadrilateral and the midpoint of the diagonals are the vertices of a parallelogram. Prove that using vectors.

If the opposite sides of a quadrilateral and also its diagonals are equal, then each of the angles of the quadrilateral is

Prove that the lines joining the middle points of the opposite sides of a quadrilateral and the join of the middle points of its diagonals meet in a point and bisect one another

If the opposite sides of a quadrilateral are equal, prove that the quadrilateral is a parallelogram.

If two opposite sides of a cyclic quadrilateral are equal,then the other two sides are parallel.

Prove that the lines joining the middle points of opposite sides of a quadrilateral and the line joining the middle points of its diagonals meet in a point and bisect one another.

If two opposite sides of a cyclic quadrilateral are equal; then the other two sides are parallel.

The midpoints of the sides of a triangle along with any of the vertices as the fourth point makes a parallelogram of area equal to

If the diagonals of a quadrilateral bisect each other; then the quadrilateral is a parallelogram.

If the diagonals of a quadrilateral bisect each other,then the quadrilateral is a parallelogram.