perplexus.info :: Geometry : Squaring sides

Squaring sides (Posted on 2005-05-04)

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.

See The Solution Submitted by Federico Kereki

Rating: 4.0000 (2 votes)

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: The analytic geometry way (part 1 only)	nikki	2005-05-06 12:31:16
The analytic geometry way (part 1 only)	Jer	2005-05-05 17:42:01
re: 2nd proof w/ a cheat	Amon	2005-05-05 00:36:33
2nd proof w/ a cheat	nikki	2005-05-04 19:54:38

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