document.write( "Question 54032: Prove or disprove by giving a counterexample.
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Algebra.Com's Answer #36307 by AnlytcPhil(1806)\"\" \"About 
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Prove or disprove by giving a counterexample.\r\n" );
document.write( "If two medians of a triangle are of the same length, \r\n" );
document.write( "then the triangle is isosceles.\r\n" );
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document.write( "Proof:\r\n" );
document.write( "Draw triangle ABC with medians BD and CE, and label \r\n" );
document.write( "their point of intersection X (which is the centroid).\r\n" );
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" );
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document.write( "1) Medians BD and CE, and BD = CE\r\n" );
document.write( "2) BX = (2/3)(BD),\r\n" );
document.write( "   DX = (1/3)(BD),\r\n" );
document.write( "   CX = (2/3)(CE), \r\n" );
document.write( "   EX = (1/3)(CE)\r\n" );
document.write( "3) BX = CX, DX = EX\r\n" );
document.write( "4) Angle BXE = Angle CXD\r\n" );
document.write( "5) Triangle BXE is congruent to Triangle CXD\r\n" );
document.write( "6) BE = CD\r\n" );
document.write( "7) 2(BE) = 2(CD)\r\n" );
document.write( "8) AB = AC\r\n" );
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document.write( "Reasons:\r\n" );
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document.write( "1) Given\r\n" );
document.write( "2) The medians of a triangle intersect \r\n" );
document.write( "   in a point that is 2/3 of the distance \r\n" );
document.write( "   from each vertex to the midpoint of \r\n" );
document.write( "   the opposite side.\r\n" );
document.write( "3) Substitution property\r\n" );
document.write( "4) Vertical angles are congruent\r\n" );
document.write( "5) Side-angle-side\r\n" );
document.write( "6) Corresponding parts of congruent triangles\r\n" );
document.write( "   are 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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