Prove that if both pairs of opposite sides of a quadrilateral are equal, then it is a parallelogram.

Prove that the quadrilatral formed by joining the mid points of the sides of a quadrilateral is a parallelogram.

Show that the diagonals of a quadrilateral bịsect each other if and only if it is a parallelogram.

Given statement in (a) and (b). Identify the statements given below as contrapositive or converse of each other . If the quadrilateral is a parallelogram then its diagonals bisect each other 1 )If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram 2) if the diagonals of a quadrilateral bisect eachother , then it is a parallogram

Calculate the length of sides of quadrilateral. .

Whether the sentence is statement: The sides of a quadrilateral have equal length.

In the figure, squareP=90^o . Sides of triangle APC are extended to B and D. Prove that, the circles drawn with the sides of a quadrilateral with perpendicular diagonals, will meet at a common point. .

Prove that any outer. angle of a cyclic quadrilateral is equal to the interior angle, at the opposite vertex.

The coordinates of the vertices of a quadrilateral taken in order are '(2,1)', '(5,3),(8,7),(4,9)'. i) Find the coordinates of the midpoints of all four sides. ii) Prove that the quadrilateral got by joining these mid points is a parallelogram.

Prove that any outer angle of a cyclic quadrilateral is equal to the inner angle at the opposite vertex.