A quadrilateral has one pair of opposite angles that are supplementary if and only if it is cyclic. Use this to determine the condition(s) why a kite is considered cyclic. Then, write
Kite - Polytope Wiki
Kite definition, basic theorems, properties
A kite is a parallelogram only when it is a rhombus.
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Parallelogram, Trapezium and Kite with Image Representation