Properties of the Deltoid: Determine whether or not it can be inferred

The quadrilateral ABCD is shown below.

Angle DCA is equal to angle BCA.

Is the quadrilateral a rhombus?

Yes, if AB = AD and DC = CB

Can we determine that the shape below is a deltoid from the data provided?

No, we need to know that BC = C.

DE = EC

Is ADBC is a kite?

Yes, if AD = AC

Which of the quadrilaterals in the diagram is a necessarily a kite?

ABCE + ABCD + AECD