Four Sided	Exactly Two Sets of Parallel Sides	At Least One Set of Parallel Sides	All Sides Are Equal Length	Both Sets of Opposite Sides are Equal Length	At Least one Set of Opposite Sides are equal length	Each Interior Angle = 90	Opposite Angles are Congruent	Base Angles are Congruent
Quadrilateral	X
Parallelogram	X	X	X		X	X		X
Rectangle	X	X	X		X	X	X	X	X
Square	X	X	X	X	X	X	X	X	X
Rhombus	X	X	X	X	X	X		X
Trapezoid	X		X
Isosceles Trapezoid	X		X			X			X

 

What's the point?  Consider the general quadrilateral.  The only minimum property of a quadrilateral is that is has 4 sides.    All other shapes listed have "four sided" as a minimum characteristic.  Are they all quadrilaterals?  Yes!  So, from this chart, you can start to get an idea of the relationships between the quadrilaterals.
 

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