document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=488188>Question 488188</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having trouble with the following problem, apparently in solving this solution I was told that the proof was oversimplified and more information was needed. I'm at a lost, any help you can give would be greatly appreciated. \r<BR>\n" );
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document.write( "Thank you.\r<BR>\n" );
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document.write( "Given: Triangle BAD is congruent to Triangle CAD<BR>\n" );
document.write( "AD is perpendicular to BC\r<BR>\n" );
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document.write( "Prove: Triangle ABC is isosceles\r<BR>\n" );
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document.write( "My solution: \r<BR>\n" );
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document.write( "Triangle BAD is congruent to Triangle CAD (statement) Given (reason)<BR>\n" );
document.write( "AD is perpendicular to BC (statement) Given (reason)<BR>\n" );
document.write( "BA is congruent to AC (statement) Corresponding parts of congruent triangles (reason)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333286 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=333286\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C0%2C10%2C0%2C10%2C%0D%0A%0D%0A%0D%0Atriangle%282%2C5%2C8%2C5%2C4%2C8%29%2C%0D%0Atriangle%282%2C5%2C8%2C5%2C4%2C2%29%2C%0D%0Alocate%282%2C5%2CA%29%2C%0D%0Alocate%288%2C5%2CD%29%2C%0D%0Alocate%284%2C8%2CB%29%2C%0D%0Alocate%284%2C2%2CC%29%2C%0D%0Aline%284%2C8%2C4%2C2%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If we assume that the labeling in the problem (\"Given triangle BAD is congruent to triangle CAD\") is correct, then right away we can claim BA = CA and triangle ABC is isosceles (you might want to say BA = CA --> ABC is isosceles in your proof).\r<BR>\n" );
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document.write( "If the labeling is incorrect (e.g. triangle BAD is actually congruent to triangle CDA\") then that is a mistake on the textbook. Just make sure you also label your points correctly, matching corresponding ones next to each other.\r<BR>\n" );
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document.write( "Either way, you would want to specify that BA = CA implies that triangle ABC is isosceles. </SPAN>\n" );
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