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.

Prove using vectors the mid-points of two opposite sides of a quadrilateral and the mid-points of the diagonals are the vertices of a parallelogram.

Connecting the midpoints of opposite sides of any quadrilateral to the midpoints of the adjacent sides must always create which of the following ?

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

prove that the line segment joining the midpoints of two opposite sides of a parallelogram divides the parallelogram into two parallelograms with equal area.

Prove that if two opposite angles and two opposite sides of any quadrilateral be parallel , then it is a parallelogram.

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 each pair of opposite sides of a quadrilateral is equal, then prove that it is a parallelogram.

If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.

If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.

If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.