document.write( "Question 831102: RAT is a triangle. [AM] is the median and O is the midpoint of [AM]
\n" ); document.write( "(RO) cuts [AT] at D. Let I be the midpoint of [TD].\r
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Algebra.Com's Answer #501202 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Two things you need to know about this proof:\r\n" );
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document.write( "A \"midsegment\" of a triangle is a segment that connects the midpoints of two\r\n" );
document.write( "sides of a triangle.\r\n" );
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document.write( "A midsegment of a triangle is parallel to the third side and is half the length\r\n" );
document.write( "of the third side.\r\n" );
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document.write( "∥ΔΔߛ ߜθθθθθσΔΔΔ⌀⎣ ⎦ ᑎ≤≥≦≧≅∠Δ\r\n" );
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document.write( "Here's an outline for the proof, you'll have to write a two-column\r\n" );
document.write( "proof yourself.\r\n" );
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document.write( "Two segments marked the same above are given equal by definition \r\n" );
document.write( "of median and midpoint.\r\n" );
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document.write( "MI is a midsegment of ΔRDT, so \"MI=expr%281%2F2%29RD\"\r\n" );
document.write( "and RD ∥ MI and so OD ∥ MI, and since AO = OM, AD = DI.\r\n" );
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document.write( "So we now know that OD is a midline of ΔMAI.\r\n" );
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document.write( "So these three segments DA, DI, and IT are all equal: \r\n" );
document.write( "DA = DI = IT, So it's immediate that \"TD=2DA\".\r\n" );
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document.write( "Since we now know that OD is a midline of ΔMAI, OD is half\r\n" );
document.write( "of MI, and MI is half of RD, so \"OD+=expr%281%2F4%29RD\",\r\n" );
document.write( "because half of a half is a fourth.\r\n" );
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document.write( "Now go write up the two-column proof.  If you have any\r\n" );
document.write( "questions about the above, ask them in the thank-you note \r\n" );
document.write( "and I'll get back to you.  BTW I don't charge any money, \r\n" );
document.write( "I'm a retired prof and just do this for fun.\r\n" );
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document.write( "Edwin

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