Students will learn how to identify squares, rectangles, rhombuses, and parallelograms from four given coordinates, using distances and the slope formula. The easiest case is to identify a square or rectangle which is axis-aligned, such as when the coordinates are (-1,1), (3,1), (3,5), (-1,5). The second easiest case is to identify a parallelogram having two of its sides axis-aligned. Here's an example problem:
Problem: Prove P(0,0), Q(4,0), R(7,4), S(3,4) is a parallelogram.
Solution: PQ and SR are parallel because both are horizontal line segments. PS is parallel to QR because Sx - Px = Rx - Qx and Sy - Py = Ry - Qy.