State whether the statements are True or False.

(i) Each angle of a rectangle is a right angle.
(ii) The opposite sides of a trapezium are parallel.

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Solution

(i) True
Adjacent sides of a rectangle are perpendicular to each other and the angle formed between perpendicular lines is a right angle.
A rectangle has 4 interior angles. Therefore all angles in a rectangle are right-angles.

(ii) False

Only one pair of opposite sides in a trapezium is parallel, not both the pairs.

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State whether the statements are true or false.

A triangle cannot have two right angles.

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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