document.write( "Question 129774: Triangle ABC is not isoceles. Prove that altitude BD would not bisect AC. \n" ); document.write( "

Algebra.Com's Answer #94786 by MathLover1(20855) $\"\"$ $\"About$

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If you construct the altitude you will see that the sides $\"AB\"$ and $\"CB\"$ are $\"not\"$ $\"+congruent\"$ .
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\n" ); document.write( "I think the way to prove $\"opposite\"$ will be best way to shove that altitude $\"BD\"$ would $\"not\"$ bisect $\"AC\"$ .\r
\n" ); document.write( "\n" ); document.write( "So, let's assume that the altitude $\"does\"$ bisect $\"AC\"$ .
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\n" ); document.write( "Then $\"AD\"$ and $\"DC\"$ are $\"congruent\"$ (by the def. of bisector),\r
\n" ); document.write( "\n" ); document.write( " so triangles $\"BAD\"$ and $\"BDC\"$ are congruent (by the side-angle-side theorem)
\n" ); document.write( " if $\"BA\"$ and $\"BC\"$ are $\"congruent\"$ , then $\"ACB\"$ $\"is\"$ $\"+isosceles\"$
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\n" ); document.write( "Hence, if the $\"altitude\"$ bisects $\"AC\"$ , then the triangle $\"must\"$ $\"+have+\"$ $\"been+\"$ $\"isosceles\"$ to start with.\r
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