document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=96363>Question 96363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HOW MANY DIAGONALS CAN BE DRAWN FROM ONE VERTEX OF A REGULAR OCTAGON? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #70227 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=70227\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Although it is true that from any vertex of a regular octagon lines can be drawn to 7 other <BR>\n" );
document.write( "vertices, those lines are NOT diagonals.<BR>\n" );
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document.write( "In a regular octagon, from a vertex you can only draw 5 diagonals. A line from a vertex to the next <BR>\n" );
document.write( "adjacent vertex on either side is not a diagonal.<BR>\n" );
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document.write( "Let's use something you are familiar with. If you are given a square (which has four <BR>\n" );
document.write( "sides and is a quadrilateral), how many diagonals can you draw from one corner? The answer <BR>\n" );
document.write( "is 1 diagonal from that corner, not 4 - 1 = 3. From one vertex in a square the only<BR>\n" );
document.write( "diagonal you can draw is from that vertex to the vertex in the opposite corner.<BR>\n" );
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document.write( "In fact, for any regular geometric figure the answer to this question is N - 3 where N is <BR>\n" );
document.write( "the number of sides of the given figure.<BR>\n" );
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document.write( "So, from one vertex in:<BR>\n" );
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document.write( "a regular triangle you can draw  3 - 3 = 0 diagonals<BR>\n" );
document.write( "a regular quadrilateral you can draw 4 - 3 = 1 diagonal<BR>\n" );
document.write( "a regular pentagon you can draw 5 - 3 = 2 diagonals<BR>\n" );
document.write( "a regular hexagon you can draw 6 - 3 = 3 diagonals<BR>\n" );
document.write( "a regular heptagon you can draw 7 - 3 = 4 diagonals<BR>\n" );
document.write( "a regular octagon you can 8 - 3 = 5 diagonals<BR>\n" );
document.write( "and so on<BR>\n" );
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document.write( "Hope this helps you to see why the answer to your problem is 5 diagonals, not 7.<BR>\n" );
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