document.write( "Question 1177132: given: triangle abc is scalene
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\n" ); document.write( "\n" ); document.write( "prove: ae is not congruent to cd
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Algebra.Com's Answer #850530 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "given: triangle ABC is scalene
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\n" ); document.write( "\n" ); document.write( "prove: AE is not congruent to CD
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document.write( "The fact that triangle ABC is a scalene means that there is no congruent pair of sides.\r\n" );
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document.write( "The area of triangle ABC is\r\n" );
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document.write( "    area = (1/2)*|BC|*|AE| = (1/2)*|AB|*|CD|.    (1)\r\n" );
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document.write( "Assume for a minute that AE is congruent to CD.\r\n" );
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document.write( "Then from equality (1), by canceling equal factors (1/2), |AE| and |CD|, we get\r\n" );
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document.write( "    |BC| = |AB|.\r\n" );
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document.write( "But it contradicts to the given fact that triangle ABC is scalene.\r\n" );
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document.write( "The contradiction proves that AE is not congruent to CD.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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