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

The opposite angles of a cyclic quadrilateral are ……………

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 that opposite angles of a cyclic quadrilateral are supplementary

Prove that if each diagonal of a quadrilateral bisects it into two triangles of equal areas, then it is a parallelogram.

Prove that if the external angle obtained by producing the side of a quadrilateral is equal to the internally oppoiste angle, then the quadrilatera wil be cyclic.

Prove that the opposite angles of a cyclic quadrilateral are suplemenary.

Prove that the quadrilateral formed by joining the mid-points successively of any quadrilateral is also a parallelogram. Also, prove that the perimeter of that parallelogram is equal to the sum of that quadrilateral's diagonals.

If the degree measure of the sum of any two opposite angles of a quadrilateral is ………….. ,then it is a cyclic quadrilateral.

If the opposite angles of any quadrilateral be supplementary, then the vertices of the quadrilateral are concyclic.

Prove that two adjacent angles of any parallel side of an isoceles trapezium are equal.