document.write( "Question 571345: How do i prove all the angles of a pentagon are congruent if i know that there are five congruent sides and 3 congruent angles? \n" ); document.write( "

Algebra.Com's Answer #368066 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "There are two cases.  One case is when the three angles that are given\r\n" );
document.write( "congruent are adjacent (the first figure below), and the other case is \r\n" );
document.write( "when they are not (the second figure below.   Mostly I will give only\r\n" );
document.write( "the steps.  You must give the reasons.   \r\n" );
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document.write( "Case 1:\r\n" );
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document.write( "Given: AB ≅ BC ≅ CD ≅ DE ≅ EA\r\n" );
document.write( "       ∠A ≅ ∠B ≅ ∠E  \r\n" );
document.write( "        \r\n" );
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document.write( " 1. Draw BE, BD and EC\r\n" );
document.write( " 2. AB ≅ BE                      (Given)\r\n" );
document.write( " 3. ᐃABE is isosceles\r\n" );
document.write( " 4. ∠ABE ≅ ∠AEB\r\n" );
document.write( " 5. ∠ABC ≅ ∠AED                      (Given) \r\n" );
document.write( " 6. m∠ABC - m∠ABE = m∠AED - m∠AEB\r\n" );
document.write( " 7. ∠CBE ≅ ∠DEB\r\n" );
document.write( " 8. BE ≅ BE\r\n" );
document.write( " 9. BC ≅ ED                          (Given)\r\n" );
document.write( "10. ᐃBCE ≅ ᐃEDB                      SAS\r\n" );
document.write( "11. BD ≅ EC\r\n" );
document.write( "12. BC ≅ ED                          (Given)\r\n" );
document.write( "13. CD ≅ CD\r\n" );
document.write( "14. ᐃBCD ≅ ᐃEDC                     SSS \r\n" );
document.write( "15. ∠BCD ≅ ∠EDC\r\n" );
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document.write( "-------------------------------\r\n" );
document.write( "Case 2.\r\n" );
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document.write( "Given: AB ≅ BC ≅ CD ≅ DE ≅ EA\r\n" );
document.write( "       ∠A ≅ ∠C ≅ ∠D \r\n" );
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document.write( " 1. Draw BE, BD and EC\r\n" );
document.write( " 2. ∠BCD ≅ ∠EDC               given\r\n" );
document.write( " 3. BC ≅ DE                   given \r\n" );
document.write( " 4. CD ≅ CD                \r\n" );
document.write( " 5. ᐃBCD ≅ ᐃEDC               SAS\r\n" );
document.write( " 6. BD ≅ EC\r\n" );
document.write( " 7. BC ≅ DE                   given\r\n" );
document.write( " 8. BE ≅ BE\r\n" );
document.write( " 9. ᐃBCE ≅ ᐃEDB\r\n" );
document.write( "10. AB ≅ AE                   given\r\n" );
document.write( "11. ᐃABE is isosceles\r\n" );
document.write( "12. ∠ABE ≅ ∠AEB\r\n" );
document.write( "13. ∠DBE ≅ ∠BEC\r\n" );
document.write( "14. ∠CBD ≅ ∠DEC\r\n" );
document.write( "15. m∠ABE + m∠DBE + m∠CBD = m∠AEB + m∠BEC + m∠DEC\r\n" );
document.write( "16. ∠ABC ≅ ∠AED\r\n" );
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document.write( "Edwin

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