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  • The quadrilateral formed by joining the mid points of the sides of a quadrilateral PQRS taken in order is a rectangle. If (A) PQRS is a rectangle (B) PQRS is a parallelogram (C) Diagonals of PQRS are perpendiculars (D) Diagonals of PQRS are equal

The quadrilateral formed by joining the mid points of the sides of a quadrilateral PQRS taken in order is a rectangle. If

(A) PQRS is a rectangle

(B) PQRS is a parallelogram

(C) Diagonals of PQRS are perpendiculars

(D) Diagonals of PQRS are equal

Answers (1)

best_answer

Answer: [C]

Solution.
According to question quadrilateral, ABCD is formed by joining the midpoints of PQRS
\Rightarrow  If PQRS is a rectangle

Here ABCD is not a rectangle because a rectangle is a four-sided polygon having all the internal angles = 90^{\circ} and the opposite sides are equal in length.
\RightarrowIf PQRS is a parallelogram

Here ABCD is not a rectangle because a rectangle is a four-sided polygon having all the internal angles = 90^{\circ} and the opposite sides are equal in length.
If diagonals of PQRS are perpendicular

Here ABCD is a rectangle because here
\angle A=\angle B=\angle C=\angle D=90^{\circ} and opposite sides we equal that is AB = DC and AD = BD
If diagonals of PQRS are equal

ABCD is not a rectangle it is a square
Because here AB = BC = CD = AD and \angle A=\angle B=\angle C=\angle D=90^{\circ}
Here we saw that if diagonals of PQRS are perpendicular to each other then ABCD is a rectangle
option C is correct
(C) diagonals of PQRS are perpendicular

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