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

Answer: 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.

Explanation:

Answer 2

A square is a special parallelogram that has 4 congruent sides and 4 right angles. Using the distance formula, you can prove that all 4 sides have a length of the square root of 8. This proves the parallelogram is a rhombus. Next, find the slope of all 4 sides. The slopes of sides AB and CD are –1, and the slopes of sides BC and DA are 1. Since adjacent sides have opposite reciprocal slopes they are perpendicular and form right angles. This proves that parallelogram ABCD is a square.

Explanation:

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