Question 936029: How do you prove that the diagonals of a parallelogram bisect each other?
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20850)   (Show Source):
Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! Consider parallelogram ORPQ with diagonals PR and OQ, the coordinates of the end points are O(0,0), R(a,0), P(b,c), Q(a+b,c). Now to prove that OP and QR bisect each other, we need to show that the diagonals have the same midpoint.
The Midpoint Formula says, if you need to find the point that is exactly halfway between two given points, just average the x-values and the y-values.
This proof is the algebraic proof, so here we go
By the midpoint formula, the midpoint of PR has coordinates ((a+b)/2, c/2).
Similarly, the midpoint of OQ has coordinates ((a+b)/2, c/2).
Since the midpoint of the two diagonals are equal, the theorem is proved.
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