document.write( "Question 536051: Show that the bisectors of angles of a parallelogram encloses right a ractangle \n" ); document.write( "

Algebra.Com's Answer #352123 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "Given: \r\n" );
document.write( "ABCD is a parallelogram\r\n" );
document.write( "AE bisects ∠BAD\r\n" );
document.write( "BF bisects ∠ABC\r\n" );
document.write( "CG bisects ∠BCD\r\n" );
document.write( "DH bisects ∠ADC\r\n" );
document.write( "To prove:\r\n" );
document.write( "LKJI is a rectangle\r\n" );
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document.write( "I will just give an outline of how to prove it. You will have to\r\n" );
document.write( "write it up as a two-column proof:\r\n" );
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document.write( "∠BAD + ∠ABC = 180° because adjacent angles of a parallelogram are supplementary\r\n" );
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document.write( "∠BAJ = ∠BAD because AE bisects ∠BAD       \r\n" );
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document.write( "∠ABJ = ∠ABC because DH bisects ∠ABC\r\n" );
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document.write( "∠BAJ + ∠ABJ = 90°  halves of supplemetary angles are complementary\r\n" );
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document.write( "ᐃABJ is a right triangle because its acute interior angles are complementary\r\n" );
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document.write( "Similar use ᐃCDL to prove ∠DLC = 90°\r\n" );
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document.write( "Similarly use ᐃADI to prove ∠AID = 90°\r\n" );
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document.write( "Then ∠JIL = 90° because ∠AID and ∠JIL are vertical angles\r\n" );
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document.write( "Then since 3 angles of quadrilateral LKJI are right angles, so\r\n" );
document.write( "is the 4th one and so LKJI is a rectangle, since its interior \r\n" );
document.write( "angles are all right angles.\r\n" );
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document.write( "Edwin

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