State true or false: Every trapezium is a parallelogram.

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True

False

answer is B.

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Detailed Solution

Given a statement, every trapezium is a parallelogram.
We need to find whether the given statement is true or false.
A trapezium or a trapezoid is a quadrilateral with exactly one pair of opposite sides as parallel.
The other pair of opposite sides are non-parallel and are called the legs of the trapezium.
Next, a parallelogram is a quadrilateral in which both the pairs of opposite sides are parallel and equal to each other. So, we can say that it is necessary for any quadrilateral to be a parallelogram, that its pair of opposite sides should be parallel and equal to each other.
But, as stated in the definition of a trapezium above, only one pair of opposite sides are parallel and not the other one.
Also, the parallels are never equal in length.
These properties differentiate a trapezium from a parallelogram.
Thus, we conclude that every trapezium is not a parallelogram, as the necessary condition for being a parallelogram is not fulfilled by a trapezium.
Hence, the given statement is false.
Hence, the correct option is (2).

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