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

If each pair of opposite sides of a quadrilateral is equal, then prove that it is a parallelogram.

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

State the converses of the following statement. In each case, also decide whether the converse is true or false.:- If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.

If the opposite sides of a quadrilateral are equal, prove that the quadrilateral is a parallelogram.

Theorem 8.5 : If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.

Apply vectors to prove that if a pair of opposite sides of quadrilateral are equal and parallel, then the figure is a parallelogram.

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

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

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)