Симетрії в дельтоїді

A kite is a quadrilateral with perpendicular diagonals and two adjacent sets of equal sides.

Clearly ABCD is a kite with CB=CD, AB=AD, and BD perpendicular to AC.

By SSS congruency, triangles ADC, ABC are congruent.

Since angles $DCA, ACB$ and angles $DAC,BAC$ are congruent, AC is an axis of which the kite is symmetric about.

Kites do not possess other symmetries.