Question

A parallelogram has vertices A(0, 4), B(2, 2), C(4, 4), and D(2,6). Is this parallelogram a square? Explain why or why not.

Answer 1

If we take the adjacent side AD and DC and work out their slopes we get

AD = (6-4)/(2-0) = 1 and DC has slope (6-4)/(2-4) = -1 . This shows that the angle between the 2 lines is 90 degrees so it looks like this is a square. If you include the slopes of each adjacent line they are at right angles too. Now to prove its a square each line must be of equal length and you'll find this is the case too.