Question

PQRS is a quadrilateral whose diagonal bisect each other at right angles


PQRS is a rectangle


PQRS is a rhombus


PQRS is a Square


None of these​

Answer 1

Answer:

PQRS is a rhombus

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Since, the diagonals AC and BD of quadrilateral ABCD bisect each other at right angles.

∴ AC is the ⊥ bisector of line segment BD

⇒ A and C both are equidistant from B and D

⇒ AB = AD and CB = CD ….(i)

Also, BD is the ⊥ bisector of line segment AC

⇒ B and D both are equidistant from A and C

⇒ AB = BC and AD = AD ……(ii)

From (i) and (ii), we get

AB = BC = CD = AD

Thus, ABCD is a quadrilateral whose diagonals bisect each other at right angles and all four sides are equal.

Hence, ABCD is a rhombus.

Hence proved.