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Diagonals of Parallelogram

Mon 17 May, 2021 09:43 pm
Prove that the diagonals of the parallelogram
in the figure intersect at their midpoints.

Here are the given points:

(0, 0), (b, c), (a + b, c), (a, 0)

All points with the exception of the origin are given in quadrant 1.

How is this done?

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engineer

1
Tue 18 May, 2021 04:47 am
Use the midpoint formula you used in this post to compute the midpoints of the two diagonals and see if they are the same.

1
Tue 18 May, 2021 04:55 pm
@engineer,
Hello. Thanks. I am looking for the same distance of the diagonals by using the midpoint formula, right?
engineer

1
Tue 18 May, 2021 07:12 pm
You are looking for the midpoints to be the exact same

1
Tue 18 May, 2021 11:26 pm
@engineer,
Ok. Sounds good.

Let me see.

Let M_1 = midpoint of points (0, 0) & (a + b, c).

Let M_2= midpoint of the points (b, c) & (a, 0).

I will not show the work.

M_1 = [(a + b + 0)/2, (c + 0)/2]

M_1 = [(a + b)/2, (c/2)]

M_2 = [(a + b)/2, (c + 0)]

M_2 = [(a + b)/2, (c/2)]

I see that M_1 = M_2.

Thus, the prove has been shown to be true.
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