document.write( "Question 1006411: \n" ); document.write( "

Algebra.Com's Answer #622557 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Two column proof.\r\n" );
document.write( "Given: CD is an altitude of ABC, D is the midpoint of BA,\r\n" );
document.write( "Prove: Triangle CDA = Triangle CDB\r\n" );
document.write( "What i think is\r\n" );
document.write( "1. CD is an altitude of ABC         - Given\r\n" );
document.write( "2. D is the midpoint of BA.         - Given\r\n" );
document.write( "3. Angle ACD = Angle BCD            - def of bisected angle  <----- The condition says nothing about bisection angle. It is not given\r\n" );
document.write( "4. Angle CD = Angle CD              - reflexive property     <----- What angle? Three symbols are used to call for an angle.\r\n" );
document.write( "5. Triangle CDA = Triangle CDB      - AAS.                   <----- I'd consider this proof as false.\r\n" );
document.write( "Am i missing something?\r\n" );
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Now consider this proof:\r
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document.write( "Triangles CDA and CDB have the common side CD.\r\n" );
document.write( "They have congruent sides DB and DC (since D is midpoint of BA).\r\n" );
document.write( "The angles CDA and CDB are congruent, since they both are direct angles.\r\n" );
document.write( "Hence, the triangles CDA and CDB are congruent, in accordance with the SAS test for triangles.\r\n" );
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document.write( "Yes, it is written not in two column form - sorry.\r\n" );
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