Question

Which among the given statements is correct?

• A. The diagonals of a parallelogram are perpendicular.
• B. The diagonals of a rectangle are perpendicular to each other.
• C. If the diagonals of a quadrilateral intersect at right angles, it is not necessarily a rhombus.
• D. Every quadrilateral is either a trapezium or a parallelogram or a kite.

Answer 1

The correct option is C If the diagonals of a quadrilateral intersect at right angles, it is not necessarily a rhombus.

• Each diagonal of a parallelogram separates it into two congruent triangles, and they bisect each other. They are not necessarily perpendicular (The diagonals of a parallelogram are perpendicular only when the parallelogram is a rhombus or a square. This statement is incorrect.
• Diagonals in a rectangle bisect each other and are equal. They aren't perpendicular to each other unless the rectangle is a square. This statement is incorrect.
• The diagonals of a rhombus or a kite intersect each other at right angles. So, when the diagonals of a quadrilateral intersect each other at right angles, the quadrilateral could be a kite or a rhombus. It's not necessarily a rhombus. Hence, this statement is correct.
• Quadrilaterals with special properties have been given special names. In a parallelogram, opposite sides are equal and parallel. In a trapezium, the opposite sides are parallel. In a kite, adjacent sides are equal. If a quadrilateral has four unequal sides or just one pair of equal sides, none of which are parallel in either case, then it is neither a parallelogram nor a kite, nor a trapezium.