A quadrilateral is a parallelogram if its opposite sides are equal.

A quadrilateral is parallelogram if its opposite angles are equal.

A quadrilateral is a parallelogram, if its one pair of opposite sides are equal and parallel.

Prove that In a parallelogram, opposite side are equal

Which of the following is not true for a parallelogram ? a) Opposite sides are equal b) Opposite angles are equal c) Opposite angles are bisected by the diagonals d) Diagonals bisect each other

E , F , G , H are respectively, the mid-points of the sides A B ,B C ,C D and D A of parallelogram A B C D . Show that the quadrilateral E F G H is a parallelogram and that its area is half the area of the parallelogram, A B C Ddot

Which of the following statements are true (T) and which are false (F)? (i) In a parallelogram, the diagonals are equal. (ii) In a parallelogram, the diagonals bisect each other. (iii) In a parallelogram, the diagonals intersect each other at right angles. (iv) In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram. (v) If all the angles of a quadrilateral are equal, it is a parallelogram. (vi) If three sides of a quadrilateral are equal , it is a parallelogram. (vii) If three angles of a quadrilateral are equal, it is a parallelogram. (viii) If all the sides of a quadrilateral are equal it is a parallelogram

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

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

The given figure shows a rectangle ABDC and a parallelogram ABEF, drawn on opposite sides of AB. Prove that : (i) quadrilateral CDEF is a parallelogram, (ii) Area of quad. CDEF = Area of rec. ABDC + "Area of" ////gm.ABEF .