Question

If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a

• A. Rhombus
• B. Rectangle
• C. Square
• D. Parallelogram

Answer 1

Answer: (B), (C)

Square

Explanation for the correct option.

Option $B$: Rectangle

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all four angles are equal to 90 degrees. Hence, it is also called an equiangular quadrilateral. Diagonals of the rectangle are equal and bisect each other.

Hence, option $B$ is the correct answer.

Option $C$: Square

A square is a quadrilateral whose four sides have the same length and four same angles. Diagonals of the square are equal in length and perpendicular bisectors to each other.

Hence, option $C$ is the correct answer.

Explanation for the incorrect option.

Option $A$: Rhombus

A rhombus is a quadrilateral whose four sides have the same length. Diagonals of the rhombus are perpendicular and bisect each other but they are not equal.

Hence, option $A$ is the incorrect answer.

Option $D$: Parallelogram

A parallelogram is a quadrilateral in which the opposite sides are parallel and equal. Diagonals of the parallelogram may not be equal but bisect each other.

Hence, option $D$ is the incorrect answer.

Hence, only option $B,C$ are the correct options.