They are all 4 sided quadrilaterals
The all have 4 interior angles that add up to 360 degrees
They all have 2 diagonals
They all have a perimeter which is the sum of their 4 sides
They all will individually tessellate
They all can be split into triangles
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A quadrilateral is a polygon with four 'sides' . A parallelogram is a quadrilateral with two sets of parallel sides.
A triangle is not a quadrilateral, but a parallelogram and trapezoid are.
A square has all the properties of a rectangle and rhombus. (A square is always a rectangle.) A rectangle is not always a square but is always a parallelogram. A parallelogram is a quadrilateral (four sided figure) with both pairs of opposite sides are parallel. A rectangle is a quadrilateral with four right angles.
Polygon means many sides and is the name given to shapes that have 3 or more sides and a parallelogram is a 4 sided poylgon or a quadrilateral
A rhombus, a parallelogram, a trapezium (unless isosceles) and the most general quadrilateral.