No
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Not exactly but all quadrilaterals have 4 sides and 4 interior angles that add up to 360 degrees.
No. They are only similar in the non-mathematical sense of having four sides and four vertices.
No because a right angle triangle has different properties to an equilateral triangle
All kites are quadrilaterals, but quadrilaterals are not kites.
All parallelograms are quadrilaterals but all quadrilaterals are not necessarily parallelograms