document.write( "Question 1202961: In quadrilateral LMNT side LM congruent side LT. Bisector of angle MLN intersects, side MN in point E and bisector of
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Algebra.Com's Answer #838348 by Edwin McCravy(20062) $\"\"$ $\"About$

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document.write( "The green lines are the angle bisectors and we are to prove that the red lines\r\n" );
document.write( "are parallel.\r\n" );
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document.write( "We will use two theorems which supposedly you have proved and can use:\r\n" );
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document.write( "Theorem 1:\r\n" );
document.write( "The internal bisector of an angle of a triangle divides the opposite side\r\n" );
document.write( "internally in the ratio of the corresponding sides containing the angle.\r\n" );
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document.write( "Theorem 2:\r\n" );
document.write( "If a line divides two sides of a triangle proportionally (in the same ratio),\r\n" );
document.write( "then it is parallel to the third side.\r\n" );
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document.write( "The internal bisector LE of angle TLN of triangle TLN divides the opposite side\r\n" );
document.write( "MN internally in the ratio of the corresponding sides, LM and LN containing the\r\n" );
document.write( "angle.\r\n" );
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document.write( "The internal bisector LF of angle MLN of triangle MLN divides the opposite side\r\n" );
document.write( "TN internally in the ratio of the corresponding sides, LN and MN containing the\r\n" );
document.write( "angle.\r\n" );
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document.write( "Since side LM is congruent to side LT, the right sides of the above equations are\r\n" );
document.write( "equal, and therefore their left sides are equal also.  (The ratios are equal).\r\n" );
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document.write( "Line EF divides sides NM and NT of triangle MNT proportionally (in the same\r\n" );
document.write( "ratio), so it is parallel to the third side MT.\r\n" );
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document.write( "Edwin

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