document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=932426>Question 932426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me solve this geometric proof?  I am trying to understand it, but I have no idea how to do this proof.\r<BR>\n" );
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document.write( "Prove that if an angle bisector is also an altitude, then the triangle is isosceles.\r<BR>\n" );
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document.write( "Given: Triangle ABC, with line BD an angle bisector and altitude line AC.\r<BR>\n" );
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document.write( "Prove: Triangle ABC is isosceles.\r<BR>\n" );
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document.write( "I would draw the figure for you, but I do not know how to draw it for you on here.\r<BR>\n" );
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document.write( "Thank you so much!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #566716 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=566716\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> BD is an altitude to AC, so <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \angle BDA = \angle BDC = 90^{\circ}\"><BR>\n" );
document.write( "Also <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \angle ABD = \angle DBC\"><BR>\n" );
document.write( "By looking at right triangles BAD and BCD, it follows that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \angle BAC = \angle BCA\"> (note that these two triangles are furthermore congruent).<BR>\n" );
document.write( "Therefore triangle ABC is isosceles because two of its interior angles (BAD = BAC, and BCA) are equal.  </SPAN>\n" );
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