document.write( "Question 174472: Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram, the parallelogramis a rhombus. State your plan and give a proof. Proof must include statements and reasons.\r
\n" ); document.write( "\n" ); document.write( "Given: ABCD is a parallelogram with <1 = (w/ wavy line above it) <2.
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Algebra.Com's Answer #129660 by Edwin McCravy(20056)\"\" \"About 
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Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram, the parallelogramis a rhombus. State your plan and give a proof. Proof must include statements and reasons.
\n" ); document.write( "Given: ABCD is a parallelogram with Ð1 @ Ð2.
\n" ); document.write( "To Prove: ABCD is a rhombus.
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document.write( " 1. ABCD is a parallelogram           1. Given\r\n" );
document.write( " 2. AB || CD                           2. Opposite sides of a\r\n" );
document.write( "                                         parallelogram are parallel\r\n" );
document.write( " 3. Ð1 = Ð2                          3. Given\r\n" );
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document.write( " 4. Ð1 = Ð3                          4. Alternate interior angles\r\n" );
document.write( "                                         formed when transversal AC\r\n" );
document.write( "                                         cuts parallel lines AB and\r\n" );
document.write( "                                         CD.\r\n" );
document.write( " 5. Ð2 = Ð3                          5. Things equat to the same \r\n" );
document.write( "                                                 thing are equal to each \r\n" );
document.write( "                                                 other\r\n" );
document.write( "                                        \r\n" );
document.write( " 6. Ð2 @ Ð3                          6. Angles congruent to the\r\n" );
document.write( "                                         same angle are congruent.\r\n" );
document.write( " 7. DACD is isosceles                 7. Base angles 2 and 3 are\r\n" );
document.write( "                                         congruent\r\n" );
document.write( " 8. AD @ CD                           8. Legs of an isosceles\r\n" );
document.write( "                                         triangle are congruent\r\n" );
document.write( " 9. AD @ BC                         9. Opposite sides of a\r\n" );
document.write( "                                         parallelogram are congruent \r\n" );
document.write( "10. CD @ AB                          10. Opposite sides of a\r\n" );
document.write( "                                         parallelogram are congruent\r\n" );
document.write( "11. AB @ BC @ CD @ AD                11. By 8,9, and 10 and \"things\r\n" );
document.write( "                                         congruent to the same thing\r\n" );
document.write( "                                         are congruent to each other\".\r\n" );
document.write( "12. ABCD is a rhombus                12. All 4 sides are congruent. \r\n" );
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document.write( "Edwin
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