document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192713>Question 192713</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131437003/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> If triangle ABC is a triangle such that a^2 + b^2 = c^2, then angle BCA is a right triangle?  This is the converse to the Pythagorean Theorem. Please do not use law of cosine! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144642 by </B><A HREF=/tutors/aboutme.mpl?userid=jojo14344><B>jojo14344(1513)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jojo14344><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=144642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Tahoma\" size=1.5><BR>\n" );
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document.write( "If triangle ABC has dimensions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we want to prove angle BCA is a Right Triangle.\r<BR>\n" );
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document.write( "Remember a Square is formed by four Right Triangles, being each triangle has the same dimensions as the other triangles.\r<BR>\n" );
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document.write( "See figure below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-1%2C8%2C-1%2C8%2Cline%280%2C0%2C0%2C6%29%2Cline%280%2C6%2C6%2C6%29%2Cline%286%2C6%2C6%2C0%29%2Cline%286%2C0%2C0%2C0%29%2Cgreen%28line%280%2C2%2C2%2C6%29%29%2Cgreen%28line%282%2C6%2C6%2C4%29%29%2Cgreen%28line%286%2C4%2C4%2C0%29%29%2Cgreen%28line%284%2C0%2C0%2C2%29%29%2Cgreen%28locate%282%2C5.7%2C90%5E0%29%29%2Cgreen%28locate%28.3%2C2.5%2C90%5Eo%29%29%2Cgreen%28locate%283.5%2C.9%2C90%5Eo%29%29%2Cgreen%28locate%285%2C4%2C90%5Eo%29%29%2Cline%280%2C.3%2C.3%2C.3%29%2Cline%28.3%2C.3%2C.3%2C0%29%2Cline%285.7%2C0%2C5.7%2C.3%29%2Cline%285.7%2C.3%2C6%2C.3%29%2Cline%285.7%2C6%2C5.7%2C5.7%29%2Cline%285.7%2C5.7%2C6%2C5.7%29%2Cline%28.3%2C6%2C.3%2C5.7%29%2Cline%28.3%2C5.7%2C0%2C5.7%29%2Clocate%285%2C3%2Cc%29%2Clocate%281.5%2C1.8%2Cc%29%2Clocate%282%2C-.2%2Ca%29%2Clocate%285%2C-.2%2Cb%29%2Clocate%286.2%2C2%2Ca%29%2Clocate%286.2%2C5%2Cb%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We get the Area of the outer Square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D=%28a%2Bb%29%5E2 ALIGN=MIDDLE  ALT=\"A%5Bo%5D=%28a%2Bb%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Also,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D=c%5E2%2Bhighlight%284%281%2F2%29%28ab%29%29 ALIGN=MIDDLE  ALT=\"A%5Bo%5D=c%5E2%2Bhighlight%284%281%2F2%29%28ab%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "*Note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%281%2F2%29%28ab%29 ALIGN=MIDDLE  ALT=\"4%281%2F2%29%28ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----> Area of 4 Right Triangles outside the inner square.\r<BR>\n" );
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document.write( "Therefore,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D=A%5Bo%5D ALIGN=MIDDLE  ALT=\"A%5Bo%5D=A%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=c%5E2%2B%28cross%284%292%281%2Fcross%282%291%29%28ab%29%29 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=c%5E2%2B%28cross%284%292%281%2Fcross%282%291%29%28ab%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B2ab%2Bb%5E2=c%5E2%2B2ab ALIGN=MIDDLE  ALT=\"a%5E2%2B2ab%2Bb%5E2=c%5E2%2B2ab\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bcross%282ab%29%2Bb%5E2=c%5E2%2Bcross%282ab%29 ALIGN=MIDDLE  ALT=\"a%5E2%2Bcross%282ab%29%2Bb%5E2=c%5E2%2Bcross%282ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28a%5E2%2Bb%5E2=c%5E2%29 ALIGN=MIDDLE  ALT=\"red%28a%5E2%2Bb%5E2=c%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then, Triangle ABC has sides <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C200%2C-1%2C3%2C-1%2C5%2Ctriangle%280%2C0%2C1.5%2C4%2C1.5%2C0%29%2Cline%281.3%2C0%2C1.3%2C.3%29%2Cline%281.3%2C.3%2C1.5%2C.3%29%2Clocate%28.7%2C-.15%2Cb%29%2Clocate%281.7%2C2%2Ca%29%2Clocate%28.7%2C2.9%2Cc%29%2Cred%28locate%281.5%2C4.4%2CB%29%29%2Cred%28locate%281.7%2C.12%2CC%29%29%2Cred%28locate%28-.15%2C0%2CA%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ---> Angle BCA is Right Triangle\r<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Jojo</font>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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