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WHAT IS THE DIFFERENCE BETWEEN QUADRILATERAL AND TRAPAZIUM ?

Any 4-sided closed figure is known as quadrilateral whereas trapezium is a kind of quadrilateral having one pair of opposite sides are parallel to each other.

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Any four sided figure is a quadrilateral. All that means is that it has four sides. A trapezium is a quadrilateral - but with specific features. Simply, that two sides are parallel. Similarly a rectangle is a quadrilateral with unique characteristics. That's all.
I know it can be confusing because a square, rectangle, trapezium, parallelogram, are all quadrilaterals however each has unique feature that identify them individually.

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A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. Sometimes, the term quadrangle is used, by analogy withtriangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on. The word quadrilateral is made of the words quad (meaning "four") andlateral (meaning "of sides").

Six Quadrilaterals.svg
 
A trapezium is defined by the properties it does not have. It has no parallel sides. Any quadrilateral drawn at random would probably be a trapezium. Since it has no interesting properties beyond those of a quadrilateral, it is not used much in geometry. 

If the quadrilateral had one pair of parallel sides, it would be a trapezoid. If both pairs of sides are parallel, it would be a parallelogram. 
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