If two opposite sides of a cyclic quadrilateral are equal, then the other two sides are parallel.

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

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

Theorem 8.3 : If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.

If two sides of a cyclic quadrilateral are parallel, prove that the remaining two sides are equal and the diagonals are also equal.

If two sides of a cyclic quadrilateral are parallel, prove that the remaining two sides are equal and the diagonals are also equal. OR A cyclic trapezium is isosceles and its diagonals are equal.

If the sides of a cyclic- quadrilateral are parallel : prove that : (i) its other two sides are equal (ii) its diagonals are equal.

Complete each of the following statements by means of one of those given in brackets again each: If one pair of opposite sides are equal and parallel, then the figure is ............... (parallelogram, rectangle, trapezium) If in a quadrilateral only one pair of opposite sides are parallel, the quadrilateral is .............. (square, rectangle, trapezium) A line drawn from the mid-point of one side of a triangle .................. another side intersects the third side at its mid-point. (perpendicular to, parallel to, to meet) If one angle of a parallelogram is a right angle, then it is necessarily a .................... (rectangle, square, rhombus) Consecutive angles of parallelogram are ...................... (supplementary, complementary) If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily (rectangle, parallelogram, rhombus) if opposite angles of a quadrilateral are equal, then it is necessarily a ................... (parallelogram, rhombus, rectangle) If consecutive sides of a parallelogram are equal, then it is necessarily a ............. (kite, rhombus, square)

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.