Use the distance formula to determine whether the sides are congruent. So take every pair of consecutive vertices and apply the distance formula. So you will have which, in any, sides are congruent.
Use the slope formula to determine which sides are parallel or perpedicular or neither of those. If the slopes are equal the sides are parallel, if the product of the slopes is - 1 the sides are perpendicular. In any other case the sides are neither parallel nor perpendicular.
With that and the definitions of the shapes you will be able to classify shapes.
To write a full example would be very long .An easy one might be this:
Given the points (0,0), (2,0), (2,2) and (0,2), classify the shape.
When you apply the distance formula: you will find 2 for all the sides, so they are all congruente.
When you apply the slope formula you will find two pair of parallel sides, and the sides that intersects are perpendicular.
So, the classification of the shape is a square.
