Question

Which quadrilaterals always have diagonals that bisect opposite angels? A. Parallelograms B. Rectangles C. Rhombi D. Squares

Answer 1

All of the above

Explanation:

All of the given quadrilaterals have diagonals that bisect each other

Answer 2

C. Rhombi

D. Squares

Explanation:

You want to know which quadrilaterals always have diagonals that bisect opposite angles.

Angle bisector

In order for a diagonal of a quadrilateral to bisect opposite angles, it must be equidistant from the sides of the angles. In effect, the sides of the angle must be the same length, and the angle-bisecting diagonal must be perpendicular to the other diagonal.

This will be the case for a kite, rhombus, or square. Among the answer choices are ...

• Rhombi
• Squares

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Additional comment

A kite has two pairs of congruent adjacent sides. The angle-bisecting diagonal bisects the angle between the congruent sides. The diagonals are not necessarily the same length, and one is bisected by the other. That is, a kite is not a parallelogram.

A rhombus is a kite with all sides congruent. The diagonals bisect each other. A rhombus is a parallelogram. Both diagonals are angle bisectors.

A square is a rhombus with equal-length diagonals.