document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=483998>Question 483998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a regular pentagon, lines are drawn so that every possible pair of vertices are connected. How many triangles are in the resulting figure?\r<BR>\n" );
document.write( "\n" );
document.write( "choose the answer and explain the reason to choose your response<BR>\n" );
document.write( "35<BR>\n" );
document.write( "30<BR>\n" );
document.write( "20<BR>\n" );
document.write( "25 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #331289 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=331289\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Counting them manually is probably the easiest way to do so. Once you draw the pentagon and all its diagonals, you can find five triangles, each one having three consecutive vertices on the pentagon (e.g. V1V2V3, V2V3V4 if we label the vertices V1,...,V5). You can count six triangles in each of them, so 30 triangles. There are also five additional triangles determined by non-adjacent vertices (e.g. V1V2V4, etc.) so the answer is 35. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );