document.write( "Question 129130: In a parallelogram ABCD,the bisector of angle A also bisects BC at X.Prove that AD = 2AB \n" ); document.write( "

Algebra.Com's Answer #94403 by Edwin McCravy(20060) $\"\"$ $\"About$

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In a parallelogram ABCD,the bisector of angle A also bisects BC at X.Prove that AD = 2AB
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document.write( "Given:  parallogram ABCD, angle BAX = angle DAX, BX = CX\r\n" );
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document.write( "To prove: AD = 2AB\r\n" );
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document.write( "Extend AX and DC till they meet at Y \r\n" );
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document.write( "1. Angle BAX = Angle CYX\r\n" );
document.write( "2. Angle BAX = Angle DAY\r\n" );
document.write( "3. Angle CYX = Angle DAY\r\n" );
document.write( "4. Triangle DAY is isosceles\r\n" );
document.write( "5. Angle B = Angle D\r\n" );
document.write( "6. Triangle ABX similar to Triangle DAY\r\n" );
document.write( "7. BC = 2BX\r\n" );
document.write( "8. AY = 2AX\r\n" );
document.write( "9. DY = 2AB\r\n" );
document.write( "10. AD = DY\r\n" );
document.write( "11. AD = 2AB\r\n" );
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document.write( "1. Alternate interior angles when transversal AY \r\n" );
document.write( "   cuts parallel lines AB and DY\r\n" );
document.write( "2. Given that AX bisects angle A \r\n" );
document.write( "3. Things equal to the same thing are equal to each other\r\n" );
document.write( "4. Base angles equal\r\n" );
document.write( "5. Opposite interior angles of a parallelogram\r\n" );
document.write( "6. Two angles equal in each\r\n" );
document.write( "7. Given that AX bisects BC\r\n" );
document.write( "8. Two intersecting transversals BC and AY between \r\n" );
document.write( "   two parallel lines AB and DY are divided in the same ratio.\r\n" );
document.write( "9. Corresponding parts of similar triangles are in the same ratio.\r\n" );
document.write( "10. Legs of isosceles triange DAY are equal \r\n" );
document.write( "11. Things equal to the same thing are equal to each other.\r\n" );
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document.write( "Note: Incidentally, you could also prove that \r\n" );
document.write( "Angle A = Angle C = 60°, Angle B = Angle D = 120°\r\n" );
document.write( "but that was not asked for. \r\n" );
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document.write( "Edwin

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