Prove that the parallelogram circumscibing a circle is a rhombus.

Prove that an angle inscribed in a semi-circle is a right angle using vector method.

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Prove that twice the area of a parallelogram is equal in the area of another parallelogram formed by taking as its adjacent sides of the diagonals of the former parallelogram.

Using dot product of vectors, prove that a parallelogram, whose diagonals are equal, is a rectangle

Prove by vector method that the parallelograms on the same base and between the same parallels are equal in area.

Prove: In a parallelogram, opposite sides are equal.

Using vectors prove that the diagonals of a parallelogram bisect each other.

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.