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Question

# Complete each of the following statements by means of one of those given in brackets against each : (i) If one pair of opposite sides is equal and parallel, then the figure is ........ (parallelogram, rectangle, trapezium) (ii) If in a quadrilateral only one pair of opposite sides is parallel, the quadrilateral is ....... (square, rectangle, trapezium) (iii) A line is 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) (iv) If one angle of a parallelogram is a right angle, then it is necessarily a ...... (rectangle, square, rhombus) (v) The consecutive angle of a parallelogram is...... (supplementary, complementary) (vi) If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily a ........ (rectangle, parallelogram, rhombus) (vii) If opposite angles of a quadrilateral are equal, then it is necessarily a ........... (parallelogram, rhombus, rectangle) (viii) If consecutive sides of a parallelogram are equal, then it is necessarily a .......... (kite, rhombus, square)

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Solution

## (i) If one pair of opposite sides is equal and parallel, then the figure is the parallelogram. (ii) If in a quadrilateral only one pair of opposite sides is parallel, the quadrilateral is trapezium. (iii) A line drawn from the mid-point of one side of a triangle parallel to another side intersects the third side at its mid-point. (iv) If one angle of a parallelogram is a right angle, then it is necessarily a rectangle. (v) The consecutive angle of a parallelogram is supplementary. (vi) If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily a parallelogram. (vii) If opposite angles of a quadrilateral are equal, then it is necessarily a parallelogram. (viii) If consecutive sides of a parallelogram are equal, then it is necessarily a rhombus.

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