No, one example is a kite that DOES NOT have two right angles. It is not a cyclic quadrilateral. A kite that does have two right angles is one.
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All quadrilaterals are polygons, but not all polygons are quadrilaterals.
Not necessarily. All parallelograms are quadrilaterals but not all quadrilaterals are parallelograms. Parallelograms are more specific instances of quadrilaterals. Its like saying all squares are rectangles but not all rectangles are squares.
Yes, all rectangles are quadrilaterals because they have four sides and all quadrilaterals have four sides.
All squares are quadrilaterals. All quadrilaterals are not squares. There is no square that is not a quadrilateral.
Quadrilateral is the broader term. All kites are quadrilaterals, but not all quadrilaterals are kites.