For any quadrilateral polygon, there are FOUR (4) sides. There are FOUR angles which sum to 360 degrees.
Quadrilaterals fall into numerous types.
IRREGULAR
SQUARE
RECTANGLE
PARALLELOGRAM
RHOMBUS
TRAPEZIUM
KITE.
But all obey the above two rules.
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It is an inscribed quadrilateral or cyclic quadrilateral.
It is simply a quadrilateral - there is no special name for such a quadrilateral.
It is an arrowhead quadrilateral
There is no specific name for such a quadrilateral.
No, a square is an equilateral quadrilateral. http://en.wikipedia.org/wiki/Quadrilateral