State true or false:

A parallelogram is a rectangle.

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True

False

answer is B.

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Detailed Solution

Here, we have to decide if the statement which says that a parallelogram is a rectangle is true or not.
So, a parallelogram is a quadrilateral with both of its opposite side pairs as equal.
This is the primary condition for a quadrilateral to be called a parallelogram.
Next, both the opposite side pairs of a parallelogram as well as the opposite angle pairs are equal and the diagonals bisect each other.
But, in the case of a rectangle, it is a special parallelogram where all the interior angles are right angles.
This means that all the interior angles are equal in a rectangle, while only the opposite angle pairs are equal in a parallelogram.
Thus, we conclude that a rectangle has all the properties of a parallelogram, as it is a special parallelogram, but a parallelogram does not hold all the properties of a rectangle.
Therefore, a parallelogram cannot be called a rectangle.
Hence, the given statement is false.
Hence, the correct option is (2).

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