document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=955031>Question 955031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a way to prove the Pythagorean Theorem  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #583375 by </B><A HREF=/tutors/aboutme.mpl?userid=EdenWolf><B>EdenWolf(517)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=EdenWolf><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=EdenWolf><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=583375\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=EdenWolf&illustration_name=image5.gif\">.\r<BR>\n" );
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document.write( "First, we need to find the area of the trapezoid by using the area formula of the trapezoid.<BR>\n" );
document.write( "A=(1/2)h(b1+b2) area of a trapezoid\r<BR>\n" );
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document.write( "In the above diagram, h=a+b, b1=a, and b2=b.\r<BR>\n" );
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document.write( "A=(1/2)(a+b)(a+b)<BR>\n" );
document.write( "=(1/2)(a^2+2ab+b^2).\r<BR>\n" );
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document.write( "Now let's find the area of the trapezoid by summing the area of the three right triangles.<BR>\n" );
document.write( "The area of the yellow triangle is<BR>\n" );
document.write( "A=1/2(ba).\r<BR>\n" );
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document.write( "The area of the red triangle is<BR>\n" );
document.write( "A=1/2(c^2).\r<BR>\n" );
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document.write( "The area of the blue triangle is<BR>\n" );
document.write( "A= 1/2(ab).\r<BR>\n" );
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document.write( "The sum of the area of the triangles is<BR>\n" );
document.write( "1/2(ba) + 1/2(c^2) + 1/2(ab) = 1/2(ba + c^2 + ab) = 1/2(2ab + c^2).\r<BR>\n" );
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document.write( "Since, this area is equal to the area of the trapezoid we have the following relation:<BR>\n" );
document.write( "(1/2)(a^2 + 2ab + b^2) = (1/2)(2ab + c^2).\r<BR>\n" );
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document.write( "Multiplying both sides by 2 and subtracting 2ab from both sides we get a^2+b^2=c^2, concluding the proof. </SPAN>\n" );
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