document.write( "Question 448086: Could you please help me solve this problem?\r
\n" ); document.write( "\n" ); document.write( "Prove the Median Inequality: If M is the midpoint of side BC of triangle ABC, then AM is less than 1/2(AB+AC).\r
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Algebra.Com's Answer #308521 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor did not prove the theorem because\r\n" );
document.write( "AM is not half of BC, as he stated.  Here is the correct proof:\r\n" );
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document.write( "The other tutor came back, edited it, and gave an alternate correct proof. \r\n" );
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document.write( "Extend AM to twice its length, to D, so that AM = DM\r\n" );
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document.write( "Draw DC\r\n" );
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document.write( "       AM = DM       by construction\r\n" );
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document.write( "     ∠AMB = ∠DMC    because they are are vertical angles.\r\n" );
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document.write( "       BM = CM       because a median bisects the side it's drawn to\r\n" );
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document.write( "     ⵠABM ≅ ⵠDCM    by Side-angle-side\r\n" );
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document.write( "        AB = DC      corresponding parts of congruent triangles.\r\n" );
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document.write( "   AC + CD > AD      by triangle inequality on ⵠACD\r\n" );
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document.write( "   AC + AB > AD      substituting equals for equals.\r\n" );
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document.write( "        AD = 2AM     by construction\r\n" );
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document.write( "   AC + AB > 2AM     substituting equals for equals.\r\n" );
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document.write( "½(AC + AB) > AM      multiplying both sides by ½ .\r\n" );
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document.write( "Edwin
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