If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the points P and Q, prove that PQ is a diameter of the circle.

If two sides of a cyclic quadrilateral are parallel , prove that the other two sides are equal

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if

The diagonals of a quadrilateral A B C D are perpendicular. Show that the quadrilateral, formed by joining the mid-points of its sides, is a rectangle.

The diagonals of a quadrilateral A B C D are perpendicular. Show that the quadrilateral, formed by joining the mid-points of its sides, is a rectangle.

The angles of a quadrilateral are equal. Prove that the quadrialteral is rectangle.

Complete each of the following, so as to make a true statement: A quadrilateral has ............ sides A quadrilateral has ............ angles. A quadrilateral has ............ vertices, no three of which are.... A quadrilateral has ............ diagonals. The number of pairs of adjacent angles of a quadrilateral is ...... The number of pairs of opposite angles of a quadrilateral is ...... The sum of the angles of quadrilateral is..... A diagonals of quadrilateral is a line segment that joins two ..... vertices of the quadrilateral. The sum of the angles of a quadrilateral is ......... right angles. The measure of each angle of a convex quadrilateral is ...... 180^0dot In a quadrilateral the point of intersection of the diagonals lie lies in .... of the quadrilateral. A point is in the interior of a convex quadrilateral, if it is in the ....... of its two opposite angles. A quadrilateral is convex if for each side, the remaining.... lie on the same side of the line containing the side.

If the sides of a cyclic quadrilateral are 3,3,4,4, show that a circle be inscribed in it.

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 each diagonals of a quadrilateral separates it into two triangles of equal area then show that the quadrilateral is a parallelogram.