document.write( "Question 147189: I need an explanation of why the Pythatgorean theorem can be used only for right triangles that an 8th grader can understand. What I know is that the Pythagorean Theorem is a special case of the Law of Cosines where the Cos(c) is equal to zero which only happens when c=90 degrees. But I don't think an 8th grader has had the law of cosines yet. I'd really appreciate some help with this. Thanks. \n" ); document.write( "

Algebra.Com's Answer #107527 by Edwin McCravy(20055) $\"\"$ $\"About$

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Edwin's solution:
\n" ); document.write( "I need an explanation of why the Pythatgorean theorem can be used only for right triangles that an 8th grader can understand. What I know is that the Pythagorean Theorem is a special case of the Law of Cosines where the Cos(c) is equal to zero which only happens when c=90 degrees. But I don't think an 8th grader has had the law of cosines yet. I'd really appreciate some help with this. Thanks.
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document.write( "Suppose you had this triangle, which is not necessarily a right triangle:\r\n" );
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document.write( "You only know that  but you don't know necessarily \r\n" );
document.write( "that angle  is 90°.\r\n" );
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document.write( "Now you construct another triangle, this time a RIGHT triangle \r\n" );
document.write( "with the SAME SIZE legs,  and , but with its hypotenuse\r\n" );
document.write( " not given to be equal to :\r\n" );
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document.write( "But we know that the Pythagorean theorem DOES hold true for triangle\r\n" );
document.write( "DEF because we constructed it so that it is a right triangle with\r\n" );
document.write( "angle E being a right angle. Therefore\r\n" );
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document.write( "And we are given that\r\n" );
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document.write( "So  because both are equal to .\r\n" );
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document.write( "and we can take positive square roots of both sides:\r\n" );
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document.write( "or \r\n" );
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document.write( "Now we have all three sides of triangle  equaling \r\n" );
document.write( "all three corresponding sides of triangle , so the\r\n" );
document.write( "two triangles are congruent, and therefore angle \r\n" );
document.write( "equals angle E which equals 90°, for they are corresponding\r\n" );
document.write( "parts of congruent triangles. Therefore  is a\r\n" );
document.write( "right triangle.\r\n" );
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document.write( "Therefore all we need know is that  to be\r\n" );
document.write( "able to conclude that triangle  is a right triangle.\r\n" );
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document.write( "So the only time the Pythagorean theorem works is when we\r\n" );
document.write( "have a right triangle.\r\n" );
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document.write( "Edwin

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