document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=452054>Question 452054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Verify that the points (0,0),(a,0) and (a/2, square root symbol \"I don't know how to type it in\", with 3a/2 in it, are equilateral triangles. Then show that the midpoints of the three sides are the vertices of a second equilateral triangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #310810 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=310810\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "(0,0),(a,0) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F2 ALIGN=MIDDLE  ALT=\"a%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283a%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%283a%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "use Distance formula\r<BR>\n" );
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document.write( "(0,0) and (a,0)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%28%28a+-+0%29%5E2+%2B+%280+-+0%29%5E2%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28a+-+0%29%5E2+%2B+%280+-+0%29%5E2%29\"   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=D+=+sqrt%28a%5E2%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28a%5E2%29\"   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=D+=+a ALIGN=MIDDLE  ALT=\"D+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(a,0) and ((a/2),(sqrt((3a)/2))\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%28%28%28a%2F2%29+-+a%29%5E2+%2B+%28%28sqrt%283%29a%29%2F2%29+-+0%29%5E2%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28%28a%2F2%29+-+a%29%5E2+%2B+%28%28sqrt%283%29a%29%2F2%29+-+0%29%5E2%29\"   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=D+=+sqrt%28%28%28a%2F2%29+-+%282a%2F2%29%29%5E2+%2B+%28%28sqrt%283%29a%29%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28%28a%2F2%29+-+%282a%2F2%29%29%5E2+%2B+%28%28sqrt%283%29a%29%2F2%29%5E2%29\"   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=D+=+sqrt%28%28-a%2F2%29%5E2+%2B+%28%283a%5E2%29%2F4%29%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28-a%2F2%29%5E2+%2B+%28%283a%5E2%29%2F4%29%29\"   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=D+=+sqrt%28%28%28a%5E2%29%2F4%29+%2B+%28%283a%5E2%29%2F4%29%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28%28a%5E2%29%2F4%29+%2B+%28%283a%5E2%29%2F4%29%29\"   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=D+=+sqrt%28%28a%5E2+%2B+3a%5E2%29%2F4%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28a%5E2+%2B+3a%5E2%29%2F4%29\"   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=D+=+sqrt%28%284a%5E2%29%2F4%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%284a%5E2%29%2F4%29\"   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=D+=+sqrt%28a%5E2%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28a%5E2%29\"   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=D+=+a ALIGN=MIDDLE  ALT=\"D+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(0,0) and ((a/2), (sqrt(3)a/2))\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%28%28%28a%2F2%29+-+0%29%5E2+%2B+%28%28sqrt%283%29a%2F2%29+-+0%29%5E2%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28%28a%2F2%29+-+0%29%5E2+%2B+%28%28sqrt%283%29a%2F2%29+-+0%29%5E2%29\"   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=D+=+sqrt%28%28a%2F2%29%5E2+%2B+%28%28sqrt%283%29a%29%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28a%2F2%29%5E2+%2B+%28%28sqrt%283%29a%29%2F2%29%5E2%29\"   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=D+=+sqrt%28%28%28a%5E2%29%2F4%29+%2B+%28%283a%5E2%29%2F4%29%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28%28a%5E2%29%2F4%29+%2B+%28%283a%5E2%29%2F4%29%29\"   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=D+=+sqrt%28%28a%5E2+%2B+3a%5E2%29%2F4%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28a%5E2+%2B+3a%5E2%29%2F4%29\"   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=D+=+sqrt%284a%5E2%2F4%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%284a%5E2%2F4%29\"   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=D+=+sqrt%28a%5E2%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28a%5E2%29\"   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=D+=+a ALIGN=MIDDLE  ALT=\"D+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, since they are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=all ALIGN=MIDDLE  ALT=\"all\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+equal ALIGN=MIDDLE  ALT=\"+equal\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=equilateral ALIGN=MIDDLE  ALT=\"equilateral\"   DISABLED_style= \"max-width:90%; height:auto;\" > triangle.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );