document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=549203>Question 549203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the answer to this proof?<BR>\n" );
document.write( "Given:Isosceles triangle with a bisector of the vertex angle<BR>\n" );
document.write( "Prove: The vertex angle bisector is perpendicular to the base of the isosceles triangle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357583 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=357583\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the angle bisector of BAC intersect segment BC at point D.  \r<BR>\n" );
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document.write( "Since ray AD is the angle bisector, angle BAD = angle CAD.  <BR>\n" );
document.write( "The segment AD = AD = itself. <BR>\n" );
document.write( "Also, AB = AC since the triangle is isosceles. \r<BR>\n" );
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document.write( "Thus, triangle BAD is congruent to CAD by SAS Test.\r<BR>\n" );
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document.write( "Therefore triangle BAD = triangle CAD, and corresponding sides and angles are equal.\r<BR>\n" );
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document.write( "DB = DC, <BR>\n" );
document.write( "angle ABD = angle ACD <BR>\n" );
document.write( "angle ADB = angle ADC. From congruence of triangles, angle ADB = angle ADC.  But by addition of angles, angle ADB + angle ADC = straight angle = 180 degrees.  Thus 2 angle ADB = straight angle and angle AMB = 90 degrees = right angle.\r<BR>\n" );
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document.write( "QED\r<BR>\n" );
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document.write( "m.ananth@hotmail.ca\r<BR>\n" );
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document.write( " </SPAN>\n" );
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