Question

For which of the following, do diagonals bisect each other?

• A. Square
• B. Kite
• C. Trapezium
• D. Quadrilateral

Answer 1

The correct option is A

Square

Explanation for correct option:

Option $\left(A\right)$:

1. All four interior angles are equal to $90°$.
2. All four sides of the square are congruent or equal to each other.
3. The opposite sides of the square are parallel to each other.
4. The diagonals of the square bisect each other at $90°$.
5. The two diagonals of the square are equal to each other.
6. The diagonal of the square divides it into two similar isosceles triangles.
7. The length of the diagonals is greater than the sides of the square.

Explanation for incorrect option:

Option $\left(B\right)$:

1. A kite has two pairs of equal sides.
2. It has two pairs of congruent triangles.
3. The longer diagonal of the kite bisects the shorter one, but not vice versa.

Option $\left(C\right)$:

1. Trapezium does not have equal sides.
2. Hence, its diagonals cannot bisect each other.

Option $\left(D\right)$:

1. All types of four-sided polygons are called quadrilaterals.
2. Hence, a quadrilateral may or may not have diagonals bisecting each other.