Just want to understand: How can I prove given points are vertices of parallelogram?

Kitimbo said:
How can I prove that given points are vertices of a parallelogram?
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Determine the order of the vertices that make it a convex quadrilateral. Use the midpoint formula on
the two pairs of opposite vertices (of the diagonals). If it's a parallelogram, the two midpoints will
coincide. The diagonals of a parallelogram bisect each other.
 
Or you could find the gradients of all the sides and check that you have two pairs of sides with equal gradients (ie are parallel).
 
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