Prove that if the midpoints of the sides of a parallelogram are connected consecutively, the quadrilateral formed is a parallelogram.
What will be an ideal response?
In the figure W, X, Y and Z are the midpoints. ?B ? ?D and ?A ? ?C because opposite angles in a parallelogram are congruent. WB ? XB ? ZD ? YD and XC? YC ? WA ? ZA because BC ? AD and AB ? CD in the original parallelogram. Then WBX ? ZDY ? WAX ? XCY by SAS, Thus, by C.P.,WX ? ZY and XY? WZ so WXYZ is a parallelogram.
Mathematics
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