What shapes diagonals bisect angles?

In geometry, the shapes whose diagonals bisect the vertex angles are rhombuses and squares. In a rhombus, each diagonal not only bisects the opposite angles but also serves as an axis of symmetry. Similarly, in a square, the diagonals bisect the angles and are equal in length, providing both angle and line symmetry. Thus, both shapes exhibit this property due to their specific symmetrical characteristics.