‘Which quadrilaterals always have diagonals that bisect opposite angles? (Select all that apply-) Parallelograms Rectangles Rhombi Squares’
The Correct Answer and Explanation is:
Correct Answers: Rhombi and Squares
To determine which quadrilaterals always have diagonals that bisect opposite angles, let’s analyze the properties of each option:
- Parallelograms
A parallelogram is a quadrilateral with both pairs of opposite sides parallel. While its diagonals bisect each other, they do not necessarily bisect the angles of the parallelogram. For example, in a general parallelogram that is not a rhombus, the diagonals cross at right angles but do not divide the corner angles into equal parts. Therefore, parallelograms do not always have diagonals that bisect opposite angles. - Rectangles
A rectangle is a special type of parallelogram with four right angles. Like all parallelograms, its diagonals bisect each other. However, they do not bisect the corner angles unless the rectangle is also a square. In general, a rectangle’s diagonals are equal in length but do not divide the 90-degree angles into equal parts along the diagonals. Therefore, rectangles are not guaranteed to have diagonals that bisect opposite angles. - Rhombi
A rhombus is a parallelogram with all four sides of equal length. One defining property of rhombi is that their diagonals are perpendicular and always bisect both the angles and each other. This means each diagonal of a rhombus divides the two opposite angles it connects into two equal parts. Thus, rhombi always have diagonals that bisect opposite angles. - Squares
A square is a quadrilateral that is both a rectangle and a rhombus. It has all the properties of both: equal sides, right angles, equal diagonals, and perpendicular diagonals that bisect both each other and the angles. Therefore, squares always have diagonals that bisect opposite angles.
Conclusion: Only rhombi and squares always have diagonals that bisect opposite angles.
