document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119087>Question 119087</A>: <I><SPAN STYLE=\"word-break: break-all;\"> side AB and BC and median AD of a triangle ABC respectively proportional to the sides PQ and QR and median of triangle PQR show that traingle ABC~PQR </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87203 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=87203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember: <BR>\n" );
document.write( "to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=congruent ALIGN=MIDDLE  ALT=\"congruent\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not same as to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+similar ALIGN=MIDDLE  ALT=\"+similar\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=median ALIGN=MIDDLE  ALT=\"median\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a triangle is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=line ALIGN=MIDDLE  ALT=\"line\"   DISABLED_style= \"max-width:90%; height:auto;\" > from a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertex ALIGN=MIDDLE  ALT=\"vertex\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=midpoint ALIGN=MIDDLE  ALT=\"midpoint\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the opposite side.\r<BR>\n" );
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document.write( "Given:\r<BR>\n" );
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document.write( "Triangles <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC+ ALIGN=MIDDLE  ALT=\"ABC+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQR ALIGN=MIDDLE  ALT=\"PQR\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB ALIGN=MIDDLE  ALT=\"AB\"   DISABLED_style= \"max-width:90%; height:auto;\" > proportional to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ ALIGN=MIDDLE  ALT=\"PQ\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC ALIGN=MIDDLE  ALT=\"BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > proportional to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QR ALIGN=MIDDLE  ALT=\"QR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and median <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD ALIGN=MIDDLE  ALT=\"AD\"   DISABLED_style= \"max-width:90%; height:auto;\" > proportional to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PM ALIGN=MIDDLE  ALT=\"PM\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "to prove:\r<BR>\n" );
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document.write( "triangles<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC+ ALIGN=MIDDLE  ALT=\"ABC+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQR ALIGN=MIDDLE  ALT=\"PQR\"   DISABLED_style= \"max-width:90%; height:auto;\" > are similar\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC ALIGN=MIDDLE  ALT=\"ABC\"   DISABLED_style= \"max-width:90%; height:auto;\" >~<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQR ALIGN=MIDDLE  ALT=\"PQR\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "proof:\r<BR>\n" );
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document.write( "prove that three sides of triangles are proportional\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" > is midpoint of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC ALIGN=MIDDLE  ALT=\"AC\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then	\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD ALIGN=MIDDLE  ALT=\"AD\"   DISABLED_style= \"max-width:90%; height:auto;\" > is proportional to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PM ALIGN=MIDDLE  ALT=\"PM\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DC ALIGN=MIDDLE  ALT=\"DC\"   DISABLED_style= \"max-width:90%; height:auto;\" > proportional to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=MR ALIGN=MIDDLE  ALT=\"MR\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD+%2B+DC+=+AC ALIGN=MIDDLE  ALT=\"AD+%2B+DC+=+AC\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PM+%2B+MR+=+PR ALIGN=MIDDLE  ALT=\"PM+%2B+MR+=+PR\"   DISABLED_style= \"max-width:90%; height:auto;\" >	\r<BR>\n" );
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document.write( "we can conclude that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC ALIGN=MIDDLE  ALT=\"AC\"   DISABLED_style= \"max-width:90%; height:auto;\" > is proportional to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PR ALIGN=MIDDLE  ALT=\"PR\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "two triangles <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC ALIGN=MIDDLE  ALT=\"ABC\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQR ALIGN=MIDDLE  ALT=\"PQR\"   DISABLED_style= \"max-width:90%; height:auto;\" > have three sides that are proportional\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB ALIGN=MIDDLE  ALT=\"AB\"   DISABLED_style= \"max-width:90%; height:auto;\" > proportional to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ ALIGN=MIDDLE  ALT=\"PQ\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC ALIGN=MIDDLE  ALT=\"AC\"   DISABLED_style= \"max-width:90%; height:auto;\" > proportional to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PR ALIGN=MIDDLE  ALT=\"PR\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC ALIGN=MIDDLE  ALT=\"BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > proportional to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QR ALIGN=MIDDLE  ALT=\"QR\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "therefore triangles<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC ALIGN=MIDDLE  ALT=\"ABC\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQR ALIGN=MIDDLE  ALT=\"PQR\"   DISABLED_style= \"max-width:90%; height:auto;\" >  are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=similar+ ALIGN=MIDDLE  ALT=\"similar+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC ALIGN=MIDDLE  ALT=\"ABC\"   DISABLED_style= \"max-width:90%; height:auto;\" >~<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQR ALIGN=MIDDLE  ALT=\"PQR\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );