A square is a quadrilateral with 4 equal sides where opposite sides are parallel and adjacent sides are perpendicular.
It's a square Explanation: See solution.
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A square is a quadrilateral with 4 equal sides where opposite sides are parallel and adjacent sides are perpendicular.
Are opposite sides parallel?
Examining the figure, we notice that the y-coordinates of K and L are the same, n. Similarly, the y-coordinates of J and M are also the same, 0. Therefore, these sides are both horizontal and hence parallel.
By the same logic, the x-coordinates of J and K are the same as are the x-coordinates of M and L. Therefore, these sides are both vertical and hence parallel.
Are adjacent sides perpendicular?
We have established that we have two sets of parallel lines. One set is horizontal and the other set is vertical. Since vertical lines are perpendicular to horizontal lines, adjacent sides are perpendicular.
Are the sides equal?
Since the sides are either horizontal or vertical, we do not need the Distance Formula to calculate the length. Instead, for the horizontal sides, we subtract the smaller y-coordinate from the larger. Similarly, for the vertical sides, we subtract the smaller x-coordinate from the larger.
Length KL:& n-0=n
Length MJ:& n-0=n
Length KJ:& n-0=n
Length LM:& n-0=n
All four sides have a length of n.
Conclusion
Since opposite sides are parallel, adjacent sides are perpendicular and all sides are of equal length, we can conclude that JKLM is a square.
