My Math Forum help please ASAP

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 November 13th, 2007, 11:34 AM #1 Newbie   Joined: Nov 2007 Posts: 3 Thanks: 0 help please ASAP Assume that a quadrilateral has the following vertex points: A (a,b) B (c,d) C (e,f) and D (g,h). EFGH are the midpoints of the sides AB,BC,CD,DA. Find the coordinated of E,F,G,H and prove that EFGH is a parallelogram. do not assign munmbers to the points, use the letters.
 November 14th, 2007, 09:32 AM #2 Global Moderator   Joined: Dec 2006 Posts: 19,546 Thanks: 1754 E is ((a + c)/2, (b + d)/2). Similar results hold for F, G and H. What do you know about EF and AC, and similarly about HG and AC?
 June 13th, 2008, 06:01 PM #3 Newbie   Joined: Jun 2008 From: New Zealand Posts: 20 Thanks: 0 Re: help please ASAP The coordinates of EFGH are as follows E {(a+c)/2, (b+d)/2} F {(c+e)/2, (d+f)/2} G {(e+g)/2, (f+h)/2} H {(a+g)/2, (b+h)/2} The slope of line EF Kef is = [(b+d)/2 - (d+f)/2]/[(a+c)/2 - (c+e)/2] = (b - f)/(a - e) The slope of line GH Kgh is = [(b+h)/2 - (f+h)/2]/[(a+g)/2 - (e+g)/2] = (b - f)/(a - e) The slopes of the line EF and GH are the same, so EF and GH are parallel. For the same reason, EH and FG are parallel. So EFGH is a parallelogram

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