document.write( "Question 621234: If every vertex of a regular pentagon is connected to every other vertex, how many triangles are formed?
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Algebra.Com's Answer #390667 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "It's too hard to count them when all the diagonals are drawn in there.\r\n" );
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document.write( "So we'll just draw each diagonal only until it just touches the next\r\n" );
document.write( "diagonal or corner and does not cross another diagonal. We draw diagonal \r\n" );
document.write( "BE:\r\n" );
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document.write( "That introduces 1 triangle ABE.  We draw in diagonal BD:\r\n" );
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document.write( "That adds two triangles, BDE and BCD so we have 3 triangles so far. \r\n" );
document.write( "We draw just enough of it until it touches the first diagonal at G:\r\n" );
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document.write( "That adds 2 more triangles, ABG and AGE, so we now have 5 triangles so far.\r\n" );
document.write( "Now we'll extend that diagonal until it touches the next diagonal at H:\r\n" );
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document.write( "That adds 2 more triangles, ABH and BGH so there are now 7 triangles.  Now we  complete drawing the diagonal AC:\r\n" );
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document.write( "That adds 4 more triangles, ABC, GBC, HBC, and HCD, so now we have 11 triangles. Now we begin the diagonal AD, drawn until it touches the \r\n" );
document.write( "other diagonal at F:\r\n" );
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document.write( "That adds 3 more triangles ABF, AGF, and AFE.  So now we have 14 triangles. Next we complete diagonal AD:\r\n" );
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document.write( "That adds 5 triangles, ABD, AHD, AED, FRD, and FED, so now we have\r\n" );
document.write( "19 triangle. Now we start the last diagonal EC drawing just to the point \r\n" );
document.write( "where it touches the diagonal at J:\r\n" );
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document.write( "That adds 3 triangles, AEJ, FEJ, and EJD.  Now we have 22 triangles.\r\n" );
document.write( "Now we extend the partial diagonal to where it just touches BD at I:\r\n" );
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document.write( "That adds 3 triangles BEI, EIJ, and JID.  So now we have 25 triangles.\r\n" );
document.write( "Finally we complete the last diagonal.\r\n" );
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document.write( "That adds 6 triangles, BEC, BIC, HIC, DIC, JCD, and ECD.  So we \r\n" );
document.write( "end up with a grand total of 31 triangles. I don't think I've\r\n" );
document.write( "missed any, or counted any twice.\r\n" );
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document.write( "Edwin
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