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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 midpoints 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)

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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