document.write( "Question 1092243: In trapezoid ABCD, diagonals AC,BD intersect at M. AD is parallel to BC and MN. AD=3, BC=6, determine MN.
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Algebra.Com's Answer #706860 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "1.  Consider triangles BMC and AMD.\r\n" );
document.write( "    They are similar, since their interior angles are congruent in pairs\r\n" );
document.write( "        (it is easy consequence of parallelism of lines AD and BC).\r\n" );
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document.write( "    The similarity coefficient is  = 2 from larger to smaller.\r\n" );
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document.write( "2.  It means that AM is half of the MC length. \r\n" );
document.write( "    It implies that AM is one third of the length AC, and that MC is two third of the length of AC.\r\n" );
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document.write( "3.  The triangles ACD and MCN are similar, too,\r\n" );
document.write( "    and the similarity coefficient is   (from larger to smaller).\r\n" );
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document.write( "    So,   = ,\r\n" );
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document.write( "    and then, substituting |AD| = 3, you get   = ,\r\n" );
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document.write( "    which implies  |MN| = 2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. |MN| = 2.\r
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