In which quadrilateral do the diagonals bisect both pairs of opposite angles?

1. A rhombus is a parallelogram that has all four sides equal in length. 2. Because all four sides match, the two triangles on either side of a diagonal are congruent. 3. The diagonals of a rhombus bisect both pairs of opposite angles. 4. In a kite only the diagonal between the equal sides bisects the interior angles, so only one pair is split. 5. A rectangle has equal diagonals that bisect each other, but they do not bisect its angles. 6. A trapezium has only one pair of parallel sides and no such diagonal property at all. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 12: Euclidean geometry_