document.write( "Question 75590: what is a pythagorean theorem?
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Algebra.Com's Answer #54260 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The Pythagorean theorem states:\r\n" );
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document.write( "The square of the hypotenuse of any right triangle\r\n" );
document.write( "equals the sum of the squares of the two legs\r\n" );
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document.write( "Here's a proof:\r\n" );
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document.write( "Start with right triangle ABC\r\n" );
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document.write( "A\r\n" );
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document.write( "B      C\r\n" );
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document.write( "We are to prove that AC² = AB² + BC²\r\n" );
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document.write( "Draw a perpendicular BD from B to AC.\r\n" );
document.write( "I can only indicate it on here by the\r\n" );
document.write( "two dots.\r\n" );
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document.write( "Right triangles ABC, BCD, and ADB are \r\n" );
document.write( "all similar because they have \r\n" );
document.write( "corresponding angles equal. So \r\n" );
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document.write( " AB     AC         AC     BC \r\n" );
document.write( "---- = ----  and  ---- = ----\r\n" );
document.write( " AD     AB         BC     CD\r\n" );
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document.write( "Cross multiplying these\r\n" );
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document.write( "AB² = AC·AD  and  BC² = AC·CD\r\n" );
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document.write( "Adding equals to equals:\r\n" );
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document.write( "AB² + BC² = AC·AD + AC·CD\r\n" );
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document.write( "Factoring out AC on the right\r\n" );
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document.write( "AB² + BC² = AC(AD + CD)\r\n" );
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document.write( "But AD + CD = AC, so we\r\n" );
document.write( "can substitute AC for AD + CD\r\n" );
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document.write( "AB² + BC² = AC·AC\r\n" );
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document.write( "AB² + BC² = AC² \r\n" );
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document.write( "An example of the Pythagorean theorem:\r\n" );
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document.write( "What is the length of the diagonal of \r\n" );
document.write( "a rectangle whose width is 3 feet and\r\n" );
document.write( "whose length is 4 feet:\r\n" );
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document.write( "The diagonal and two adjacent sides of\r\n" );
document.write( "the rectangle form a right triangle, where\r\n" );
document.write( "the diagonal is the hypotenuse.\r\n" );
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document.write( "a² + b² = c²\r\n" );
document.write( "3² + 4² = c²\r\n" );
document.write( " 9 + 16 = c²\r\n" );
document.write( "     25 = c²\r\n" );
document.write( "      5 = c\r\n" );
document.write( "So the length of the diagonal is 5\r\n" );
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document.write( "Edwin
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