document.write( "Question 334070: in a quadrilateral ABCD , angle B = 90°. If $\"AD%5E2=AB%5E2%2BBC%5E2%2BCD%5E2\"$ , then prove that angle ACD = 90° \n" ); document.write( "

Algebra.Com's Answer #239389 by Edwin McCravy(20056) $\"\"$ $\"About$

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in a quadrilateral ABCD , angle B = 90°. If $\"AD%5E2=AB%5E2%2BBC%5E2%2BCD%5E2\"$ , then prove that angle ACD = 90°
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document.write( "We know that ABC is a right triangle because angle B = 90°\r\n" );
document.write( "So we can use the Pythagorean theorem on that right triangle:\r\n" );
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document.write( "We are given that \r\n" );
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document.write( "Not that the terms I've colored red are the same in both\r\n" );
document.write( "equations so we can substitute  for the two red\r\n" );
document.write( "terms in the second equation,\r\n" );
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document.write( "Now we use the converse of the Pythagorean theorem which\r\n" );
document.write( "states that the Pythagorean theorem holds ONLY for right \r\n" );
document.write( "triangles, thus triangle ACD is a right triangle and angle\r\n" );
document.write( "ACD is a right angle or 90° \r\n" );
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document.write( "Edwin

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