document.write( "Question 990717: Conjecture: The angle bisector of the vertex angle of an isosceles triangle is also a median to the base. \n" ); document.write( "
Algebra.Com's Answer #610711 by Edwin McCravy(20054)\"\" \"About 
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document.write( "The angle bisector divides it into two triangles which can\r\n" );
document.write( "be proved congruent by SAS.  One pair of congruent sides are \r\n" );
document.write( "the congruent legs of the isosceles triangle.  The angles are \r\n" );
document.write( "congruent because an angle bisector divides the angle into two\r\n" );
document.write( "congruent parts. The other pair of congruent sides is the \r\n" );
document.write( "angle bisector itself, as it is part of both triangles.  So \r\n" );
document.write( "you have SAS.\r\n" );
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document.write( "That makes the angle bisector also a bisector of the base \r\n" );
document.write( "because of corresponding parts of conruent triangles.\r\n" );
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document.write( "That is all that is needed to prove it is a median.\r\n" );
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document.write( "It is also the perpendicular bisector of the base, which you may \r\n" );
document.write( "also be asked to prove later.\r\n" );
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document.write( "To do that, you prove additionally that the angles that the angle \r\n" );
document.write( "bisector make with the base are right angles.  First, they are \r\n" );
document.write( "congruent because of corresponding parts of congruent triangles.\r\n" );
document.write( "Also they form a linear pair. Then congruent angles that form a \r\n" );
document.write( "linear pair are right angles.   \r\n" );
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document.write( "Edwin
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