Question

Which statement(s) is/are correct?
(1)The diagonals of a parallelogram are equal.
(2)The diagonals of a square are perpendicular to each other.
(3)If the diagonals of a quadrilateral intersect at right angles, it is not necessarily a rhombus.
(4)Every quadrilateral is either a trapezium or a parallelogram or a kite.

• A. Only (2)
• B. Only (3)
• C. Both (2) and (3)
• D. (1), (2) and (3)

Answer 1

The correct option is C Both (2) and (3)

$\Rightarrow$ In four given statement we have given that, the diagonals of a parallelogram are equal which is not correct because we know that in properties of parallelogram it has opposite sides parallel but it's diagonals are not equal.

$\Rightarrow$ Second statement says, the diagonals of a square are perpendicular to each other which is true because we know that square has all four sides equal, opposite sides parallel to each other and both diagonals are equal and perpendicular to each other.

$\Rightarrow$ Third statement says that, if the diagonals of a quadrilateral intersect at right angles, it is not necessarily a rhombus, which is correct because the diagonals of a square also bisect each other at right angles.

$\Rightarrow$ Fourth statement says that, every quadrilateral is either a trapezium or a parallelogram or a kite which is wrong because rectangle, rhombus and square are also types of quadrilateral.

$\Rightarrow$ So correct statements are statement ( 2) and (3) then correct option is option C.