document.write( "Question 331516: TriangleABC and Triangle DAC are two isosceles triangle with angle BAC=20 and angle ADC=100.Show that AB=BC+CD. \n" ); document.write( "
Algebra.Com's Answer #237651 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Locate point E so that triangle EAB is congruent to triangle DAC\r\n" );
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document.write( "Draw ED\r\n" );
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document.write( "Extend BC to F so that CF = CD.  Draw DF\r\n" );
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document.write( "I won't go through every step.  I'll just tell you enough so\r\n" );
document.write( "you can write it out like your teacher wants you to.  \r\n" );
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document.write( "Using the fact that isosceles triangles have equal\r\n" );
document.write( "base angles, that interior angles of a triangle have sum 180°,\r\n" );
document.write( "that supplementary angles have sum 180°, and that vertical angles \r\n" );
document.write( "are equal,  you can now write the number of degrees in every\r\n" );
document.write( "angle in the figure.  That would be a good idea.\r\n" );
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document.write( "Therefore it is easy to show that \r\n" );
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document.write( "angle EAD = 100° = angle ADC = angle AEB.\r\n" );
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document.write( "Then by SAS, triangles ADC, AEB and AED are all congruent.  So \r\n" );
document.write( "AB = ED. \r\n" );
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document.write( "It is easy to show that angle DCF = 60° and that triangle CFD is\r\n" );
document.write( "equilateral.  You then show that BFDE is a parallelogram because\r\n" );
document.write( "angle F = 60° = angle BED , angle EBF = 120° = angle EDF.  \r\n" );
document.write( "Then AB = ED = BF = BC + CF and since CF = CD, then AB = BC + CD.\r\n" );
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document.write( "If you have any questions as to why anything is true, you can ask \r\n" );
document.write( "me in your thank-you note and I'll answer.\r\n" );
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document.write( "Edwin
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