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Q.

State whether given statement is true or false:

Quadrilateral ABCD is a parallelogram and if its diagonals are perpendicular to each other, then it is a rhombus.

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a

True

b

False

answer is A.

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Detailed Solution

Let us consider the figure given below.
Question Image

Question Image

We are given that the diagonals of a given parallelogram are perpendicular to each other. We know that if diagonals of a quadrilateral are perpendicular to each other then, the quadrilateral is a rhombus.
Hence, we conclude that parallelogram ABCD is a rhombus.
Hence, the given statement is true.
So, the correct option is 1.

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