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State True/False:
Every parallelogram is a rectangle.

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True

False

answer is B.

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Detailed Solution

The above statement is False.

A parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal. The opposite angles of a parallelogram are equal.

So, in parallelogram ABCD,

AB = DC and AD = BC
∠A = ∠C and ∠B = ∠D

A rectangle is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal.

All the angles of a rectangle are 90^o.

So, in rectangle ABCD,

AB = DC and AD = BC
∠A = ∠B = ∠C = ∠D = 90^o

In a parallelogram, all angles are not equal to 90 degrees.

Therefore, every parallelogram is not a rectangle.

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