document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251610>Question 251610</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given- Isosceles triangle ABC with segment Ab congruent to segment AC<BR>\n" );
document.write( "line CD is perpendicular to AB.<BR>\n" );
document.write( "Prove- Segment BC multiplied by segment BC is equal to two times segment AB multiplied by segment BD </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183873 by </B><A HREF=/tutors/aboutme.mpl?userid=vksarvepalli><B>vksarvepalli(154)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vksarvepalli><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=vksarvepalli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=183873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> consider the triangle BCD which is a right angled triangle\r<BR>\n" );
document.write( "\n" );
document.write( "now using Pythagoras theorem we get <BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%5E2=CD%5E2+%2B+BD%5E2 ALIGN=MIDDLE  ALT=\"BC%5E2=CD%5E2+%2B+BD%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >------------1\r<BR>\n" );
document.write( "\n" );
document.write( "now consider the triangle ACD which is also a right angled triangle\r<BR>\n" );
document.write( "\n" );
document.write( "again using Pythagoras th. <BR>\n" );
document.write( "       <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC%5E2=AD%5E2%2BCD%5E2 ALIGN=MIDDLE  ALT=\"AC%5E2=AD%5E2%2BCD%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >------------2\r<BR>\n" );
document.write( "\n" );
document.write( "but AB=AC (isosceles) \r<BR>\n" );
document.write( "\n" );
document.write( "so substituting it in 2 we get<BR>\n" );
document.write( "       <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%5E2=AD%5E2%2BCD%5E2 ALIGN=MIDDLE  ALT=\"AB%5E2=AD%5E2%2BCD%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "but AB=AD+DB\r<BR>\n" );
document.write( "\n" );
document.write( "so,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AD%2BBD%29%5E2=AD%5E2%2BCD%5E2 ALIGN=MIDDLE  ALT=\"%28AD%2BBD%29%5E2=AD%5E2%2BCD%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "i.e., <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD%5E2%2BAD%5E2%2B2%2AAD%2ABD=AD%5E2%2BCD%5E2 ALIGN=MIDDLE  ALT=\"BD%5E2%2BAD%5E2%2B2%2AAD%2ABD=AD%5E2%2BCD%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "on simplifying we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD%5E2=BD%5E2%2B2%2AAD%2ABD ALIGN=MIDDLE  ALT=\"CD%5E2=BD%5E2%2B2%2AAD%2ABD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "substituting the value of CD^2 in equation 1\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%5E2=BD%5E2%2B2%2AAD%2ABD+%2B+BD%5E2 ALIGN=MIDDLE  ALT=\"BC%5E2=BD%5E2%2B2%2AAD%2ABD+%2B+BD%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "taking out BD common in the right hand side of the equation \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%5E2=2%2ABD%2A%28AD%2BBD%29 ALIGN=MIDDLE  ALT=\"BC%5E2=2%2ABD%2A%28AD%2BBD%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "but AD+BD=AB\r<BR>\n" );
document.write( "\n" );
document.write( "therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%5E2=2AB%2ABD ALIGN=MIDDLE  ALT=\"BC%5E2=2AB%2ABD\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );