document.write( "Question 936029: How do you prove that the diagonals of a parallelogram bisect each other? \n" ); document.write( "

Algebra.Com's Answer #569439 by rothauserc(4718) $\"\"$ $\"About$

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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.
\n" ); document.write( "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.
\n" ); document.write( "This proof is the algebraic proof, so here we go
\n" ); document.write( "By the midpoint formula, the midpoint of PR has coordinates ((a+b)/2, c/2).
\n" ); document.write( "Similarly, the midpoint of OQ has coordinates ((a+b)/2, c/2).
\n" ); document.write( "Since the midpoint of the two diagonals are equal, the theorem is proved.
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