document.write( "Question 192215: prove parallelogram ABCD is a rhombus(question)
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document.write( "given: AC bisects angles BAD and BCD
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document.write( "given: ABCD is a parallelogram \n" );
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Algebra.Com's Answer #144340 by orca(409)![]() ![]() ![]() You can put this solution on YOUR website! To prove the parallelogram is a rhombus you have to show that AB = BC = CD = DA.\r \n" ); document.write( "\n" ); document.write( "To prove AB = DA and BC = CD, we need to prove triangles ABC and ADC are congruent. \n" ); document.write( "Because angle BAC = angle DAC, angle BCA = angle DCA, and AC = AC, so triangles ABC and ADC are congruent. \n" ); document.write( "Hence AB = DA and BC = CD.\r \n" ); document.write( "\n" ); document.write( "Next we need to show that AB = CD, this is obvious because they are the opposite sides of a parallelogram.\r \n" ); document.write( "\n" ); document.write( "So AB = BC = CD = DA\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |