document.write( "Question 830175: Prove that any two diagonals of a regular pentagon are congruent. Are any two diagonals congruent in any regular polygon? \n" ); document.write( "
Algebra.Com's Answer #500415 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I'll just tell you how.  You can write up a two-column proof.\r\n" );
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document.write( "All sides of a regular polygon are congruent.  All interior angles of\r\n" );
document.write( "a regular polynomial are congruent.\r\n" );
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document.write( "so AB ≅ AE, BC ≅ ED, ∠B ≅ ∠E, therefore ΔABC ≅ ΔAED by SAS, \r\n" );
document.write( "so AC ≅ AD by cpct.\r\n" );
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document.write( "Draw in diagonal CE.\r\n" );
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document.write( "Now ΔCDE ≅ ΔABC by SAS and AC ≅ CE\r\n" );
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document.write( "Draw in BE\r\n" );
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document.write( "Prove ΔCDE ≅ ΔABE the same way and then BE ≅ CE\r\n" );
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document.write( "Finally draw in BD\r\n" );
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document.write( "And now ΔBCD ≅ ΔABE and so BE ≅ BD.  Now write it up as a \r\n" );
document.write( "two-column proof.\r\n" );
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document.write( "Are any two diagonals congruent in any regular polygon?\r\n" );
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document.write( "Take a look at a regular nonagon (nine sided regular polygon):\r\n" );
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document.write( "No way those two diagonals are congruent!  The only\r\n" );
document.write( "regular polygons that have all diagonals congruent are\r\n" );
document.write( "regular polygons with sides 4 and 5.  (A 4-sided\r\n" );
document.write( "regular polygon is a square).\r\n" );
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document.write( "Edwin
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