Question

State whether the given statement is true or false
All parallelograms are trapeziums
A. True
B. False

Answer 1

Hint: Here we use the definition of parallelograms and trapezium and check if all the parallelograms fulfill the criteria of being a trapezium or not.

Complete step-by-step solution:
We write definitions of both parallelogram and trapezium and see if a trapezium is a parallelogram or not.
Parallelogram:
A parallelogram is a quadrilateral having the opposite pair of sides equal and parallel. The angles opposite to each other are equal in measure.

Here ABCD is a parallelogram with parallel sides AB, CD and BC, DA.
Trapezium: A quadrilateral having one pair of opposite sides parallel is called a trapezium. We draw a rough figure of a trapezium.

Here ABCD is a trapezium is parallel sides AB and CD and non-parallel sides AD and BC. Since other pair of sides is not parallel to each other, then trapezium is not a kind of parallelogram
A trapezium is not a type of parallelogram.
Since trapezium is not even a kind of parallelogram we can clearly say that all parallelograms are not trapeziums
Hence, the statement in the question is FALSE.

So, option B is correct.

Note: Students many times make mistake of writing the answer to this question as true as they think the criteria for being a parallelogram is only one side parallel but they should keep in mind that there should be two pairs of sides that are equal as well as parallel to each other in the figure, then only it becomes a parallelogram. Here trapezium clearly states from the definition that it has only one pair of opposite sides that are parallel and are not even equal so it doesn’t fulfill the requirement of even one side being parallel and equal.