SOLUTION: the midpoint quadrilateral theorem: the quadrilateral formed bt joining the midpoints of the consecutive sides of any quadrilateral is a parallelogram how do i do the proof of t

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Question 397983: the midpoint quadrilateral theorem: the quadrilateral formed bt joining the midpoints of the consecutive sides of any quadrilateral is a parallelogram
how do i do the proof of the theorem?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Analytic proof:
Consider the quadrilateral WXYZ with the vertices W (0,0), X (a,0), Y(b, c), and Z(d,e). The midpoint of side WX is (a/2, 0), while the midpoint of side XY is ((a+b)/2, c/2). The slope of the line passing through these two midpoints is %0D%0A%280-c%2F2%29%2F%28a%2F2-%28a%2Bb%29%2F2%29+=+%28-c%2F2%29%2F%28-b%2F2%29+=+c%2Fb.
The midpoint of side YZ is ((b+d)/2, (c+e)/2), while the midpoint of side ZW is (d/2, e/2). The slope of the line passing through these two midpoints is %0D%0A%28%28c%2Be%29%2F2+-+e%2F2%29%2F%28%28b%2Bd%29%2F2+-+d%2F2%29+=+c%2Fb. These two lines\sides would constitute one pair of parallel sides of the parallelogram.
Now compute for the slope of the line connecting the midpoints of sides XY and YZ.
Compute also for the slope of the line passing through the midpoints of ZW and WX.
These two other sides would be the other pair of parallel sides of the parallelogram.