Question 260453: Given: A (4,3), B (8,3), C (9,10), and D (5,10) are vertices of a quadrilateral. Is quadrilateral ABCD a parallelogram? Use mathmatics to justify your answer. (graphing is not acceptable) .... I need an example or this answer cause im very confused....Thank you
Found 3 solutions by jim_thompson5910, richwmiller, stanbon:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! A parallelogram is a quadrilateral in which has opposite sides that are parallel to one another. Recall that parallel lines have equal slopes. So simply find the slopes of lines AB, BC, CD, and AD. If the slope of lines AB and CD are equal, and the slopes of the lines BC and AD are equal, then ABCD is a parallelogram.
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! You can graph it to help you picture the figure but you must give a mathematical answer. You can't talk about the graph per se in your answer.
We can see just by looking at the points that the length of AB is the same as the length of CD ie 4
Now you need to show that BC and AD are equal.
You also want to show that the lines (AB and CD) and (BC and AD) are parallel by showing that the slopes are the same.
If the sides are of equal length and are parallel I believe that is enough to show that it is a parallelogram.
Do you know how to do any of that?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Given: A (4,3), B (8,3), C (9,10), and D (5,10) are vertices of a quadrilateral. Is quadrilateral ABCD a parallelogram? Use mathmatics to justify your answer. (graphing is not acceptable)
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Plot the points so you can see what is happening.
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Is ABCD a parallelogram?
Check the slopes of opposite sides.
ABslope: (3-3)/(8-4)= 0
CDslope: (10-10)/(5-9) = 0
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BCslope: (10-3)/(9-8) = 7/1
ADslope: 7/1
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Opposite sides are parallel so it is a parallelogram.
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Cheers,
Stan H.
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