document.write( "Question 1023683: How many sets of congruent triangles are there when you draw all diagonals of a regular pentagon and how do you know they are congruent? \n" ); document.write( "
Algebra.Com's Answer #639173 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "There are 5 sets of congruent triangles.\r\n" );
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document.write( "I have lettered all 11 regions A through K.\r\n" );
document.write( "I will indicate triangles by writing the regions\r\n" );
document.write( "which they contain, such as A represents triangle\r\n" );
document.write( "whis is just region A.  AB will represent the\r\n" );
document.write( "triangle composed of regions A and B.  ABC will\r\n" );
document.write( "represent the triangle composed of regions A,B,\r\n" );
document.write( "and C.  ABDEI is the triangle composed of regions\r\n" );
document.write( "A,B,C,D,E, and I.\r\n" );
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document.write( "1. These 5 triangles are congruent: A≅C≅G≅J≅K\r\n" );
document.write( "2. These 5 triangles are congruent: B≅D≅F≅H≅I\r\n" );
document.write( "3. These 10 triangles are congruent: \r\n" );
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document.write( "AB≅BC≅CF≅FJ≅IJ≅IK≅HK≅GH≅GD≅AD\r\n" );
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document.write( "4. These 10 triangles are congruent: \r\n" );
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document.write( "ABC≅ADG≅GHK≅KIJ≅CFJ≅DEF≅BEH≅DEI≅EFH≅BEI\r\n" );
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document.write( "5. These 5 triangles are congruent: ABDEI≅BCEFH≅DEFIJ≅BEHIK≅DEFGH\r\n" );
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document.write( "That makes 35 triangles.\r\n" );
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document.write( "They are congruent by the law of common sense of symmetrical\r\n" );
document.write( "things. [Yes I know that's not a proof! :)  ]\r\n" );
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document.write( "It wouldn't be hard to prove any two of those congruent, but\r\n" );
document.write( "all 35?  Forget it!  If you pick two that you want me to\r\n" );
document.write( "prove congruent, I can help you do that, but proving that \r\n" );
document.write( "all pairs of congruent triangles above are really congruent \r\n" );
document.write( "is an unreasonable task that would take many hours.\r\n" );
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document.write( "Edwin
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