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Opposite Angles of a Parallelogram Are Equal

If both pairs...

Question

If both pairs of opposite angles of a quadrilateral are equal, then the quadrilateral is a parallelogram.

A

False

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B

True

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Solution

The correct option is B True

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Prove that if both pairs of opposite angles of a quadrilateral are equal, then it is a parallelogram. [3 MARKS]

Prove that if in a quadrilateral each pair of opposite Angles are equal then it is a parallelogram.

Q. Complete each of the following statements by means of one of those given in brackets against each:
(i) If one pair of opposite sides are equal and parallel, then the figure is ........................
(parallelogram, rectangle, trapezium)

(ii) If in a quadrilateral only one pair of opposite sides are parallel, the quadrilateral is ................ (square, rectangle, trapezium)

(iii) 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)

(iv) If one angle of a parallelogram is a right angle, then it is necessarily a .................
(rectangle, square, rhombus)

(v) Consecutive angles of a parallelogram are ...................
(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)

Q. If in a quadrilateral each pair of opposite angle is equal then prove that it is a parallelogram

A quadrilateral is a parallelogram, if pair of opposite sides are equal and __.

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