document.write( "Question 207420: Please help me prove that DEFH is a parallelogram and why BF=DG and CH=GE
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\n" ); document.write( "F and H are the midpoints of BG and CG respectively
\n" ); document.write( "The diagram is at the website: http://situpirelality.blogspot.com/
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Algebra.Com's Answer #157090 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "I'll just outline the proof.  You can write it out in\r\n" );
document.write( "two-column form.  The proof is mainly based on this theorem:\r\n" );
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document.write( "The segment joining the midpoints of two sides of a triangle\r\n" );
document.write( "is parallel to the third side.\r\n" );
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document.write( "Using that theorem,\r\n" );
document.write( "DE is parallel to BC because D and E are the midpoints of AB and AC \r\n" );
document.write( "in triangle ABC\r\n" );
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document.write( "FH is parallel to BC because F and H are the midpoints of GB and GC \r\n" );
document.write( "in triangle ABC\r\n" );
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document.write( "Therefore DE is parallel to FH because they are both parallel to BC\r\n" );
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document.write( "Next draw in line segment AG\r\n" );
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document.write( "DH is parallel to AG because D and H are the midpoints of AC and GC \r\n" );
document.write( "in triangle ACG\r\n" );
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document.write( "EF is parallel to AG because E and F are the midpoints of AB and BG \r\n" );
document.write( "in triangle ABG\r\n" );
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document.write( "Therefore DH is parallel to EF because they are both parallel to AG\r\n" );
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document.write( "Therefore DEFH is a parallelogram because both pairs of opposite\r\n" );
document.write( "sides are parallel.\r\n" );
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document.write( "Since the diagonals of a parallelogram bisect each other,\r\n" );
document.write( "DG = GF, and we are given that GF = BF since F is the midpoint of BG.\r\n" );
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document.write( "Similarly, GE = GH, and we are given that GH = HC since H is the midpoint of CG. \r\n" );
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document.write( "Edwin
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