Take any convex quadrilateral ABCD, with diagonals AC and BD. Pick E so ABCE is a parallelogram. Prove that AB²+BC²+CD²+DA²= AC²+BD²+DE².
Given the same quadrilateral, let P and Q be the midpoints of AC and BD. Now prove that AB²+BC²+CD²+DA²= AC²+BD²+4PQ².
(In reply to
The analytic geometry way (part 1 only) by Jer)
This is how I was trying to solve part 1 as well, but I got stuck. I think my problem was that I chose A to be at the origin and B on the x-axis. I think it makes a difference which points you put at the origin and such.
But thanks to you my solution to the second part is now valid! Yay! Donkey Kong, Yay!
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Posted by nikki
on 2005-05-06 12:31:16 |
re: The analytic geometry way (part 1 only)
