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Show that quadrilateral FGHJ is a trapezoid, but is not a parallelogram.

Show that quadrilateral FGHJ is a trapezoid, but is not a parallelogram.-example-1
User Nick Knowlson
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1 Answer

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18 votes

In order to have a parallelogram, the opposite sides need to be parallel.

And in order to be a trapezoid, just one pair of sides needs to be parallel.

Looking at the image, the sides FG and JH are parallel, since they have the same slope (we can also see that both these sides have no variation in the y-coordinate, so they are parallel).

Then, looking at the sides FJ and GH, they are not parallel, because they have different slopes (the side FJ has a run of 1 and a rise of -3, and the side GH has a run of 2 and a rise of -3).

Since the quadrilateral FGHJ has just one pair of parallel sides, it is a trapezoid but not a parallelogram.

User Deepika Lalra
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