document.write( "Question 75812: Prove that if 2 medians of a triangle are congruent then the triangle is isosceles \n" ); document.write( "
Algebra.Com's Answer #54441 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Prove that if 2 medians of a triangle are congruent \r\n" );
document.write( "then the triangle is isosceles\r\n" );
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document.write( "Construct Triangle ABC with medians BD and CE, \r\n" );
document.write( "and the centroid (intersection of the medians) as X.\r\n" );
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document.write( "Given: Medians BD and CE, and BD = CE\r\n" );
document.write( "Prove: AB = AC\r\n" );
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document.write( "Statements:\r\n" );
document.write( "1) Medians BD and CE, and BD = CE\r\n" );
document.write( "2) BX = (2/3)(BD), DX = (1/3)(BD), CX = (2/3)(CE), EX = (1/3)(CE)\r\n" );
document.write( "3) BX = CX, DX = EX\r\n" );
document.write( "4) mÐBXE = mÐCXD \r\n" );
document.write( "5) D BXE @ D CXD\r\n" );
document.write( "6) BE = CD\r\n" );
document.write( "7) 2(BE) = 2(CD)\r\n" );
document.write( "8) BD = CE\r\n" );
document.write( "Reasons:\r\n" );
document.write( "1) Given\r\n" );
document.write( "2) The medians of a triangle intersect in a point \r\n" );
document.write( "   that is two-thirds of the distance from each \r\n" );
document.write( "   vertex to the midpoint of the opposite side.\r\n" );
document.write( "3) Substitution property\r\n" );
document.write( "4) Vertical angles are congruent\r\n" );
document.write( "5) SAS postulate\r\n" );
document.write( "6) Corresponding parts of congruent triangles are \r\n" );
document.write( "   congruent\r\n" );
document.write( "7) Multiplication property of equality \r\n" );
document.write( "8) Midpoint theorem\r\n" );
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document.write( "Edwin
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