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An convex n-gon has n(n-3)/2 diagonals.

So a square is a 4-gon and it has 4(1)/2=2 diagonals.
A pentagon has 5(2)/2=5 diagonals.


quadrilaterals always have 2 diagonals.
Here is a link with some pics to help you see the various kinds they have. That is to say, are they perpendicular, to they bisect each other?

http://illuminations.nctm.org/LessonDetail.aspx?id=L655

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