Question 722838: How do you prove that the midpoints of quadrilateral will form a parallelogram using a geometric proof?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Draw an arbitrary quadrilateral on a set of coordinate axes such that one vertex is at the origin and one of the sides of the quadrilateral is coincident with the  -axis.
Label the vertices (0,0), (b, 0), (a,d), and (c,e). Use the midpoint formulas to calculate, in terms of a, b, c, d, and e, the coordinates of the midpoints of each of the four sides. Construct line segments connecting each pair of midpoints. Use the slope formula to show that the opposite sides of the figure created by these segments have identical slopes, are therefore parallel, and are therefore the sides of a parallelogram.
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John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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