document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153572>Question 1153572</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In right triangle ABC, AC = BC and ∠C = 90. Let P and Q be points on hypotenuse<BR>\n" );
document.write( "AB, such that ∠PCQ = 45°. Show that AP^2+BQ^2=PQ^2. I think the first step is<BR>\n" );
document.write( "to rotate it 90 degrees counter clockwise around C, let P go to P’ and find ∠P’CQ.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #775860 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=775860\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><font size=1>[My previous solution had some lettering that did not match the drawn figure.  I think I have corrected all the errors below.]</font>\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%282800%2F9%2C400%2C-1%2C13%2C-5%2C13%2C%0D%0A%0D%0Aline%280%2C0%2C0%2C12%29%2C%0D%0Aline%280%2C0%2C4%2C8%29%2C%0D%0Aline%280%2C0%2C9%2C3%29%2C%0D%0Aline%280%2C0%2C12%29%2C%0D%0Aline%2812%2C0%2C0%2C12%29%2C%0D%0A%0D%0Ared%28arc%280%2C0%2C4.3%2C-4.3%2C18%2C63%29%2Carc%280%2C12%2C4.3%2C-4.3%2C270%2C315%29%2Carc%2812%2C0%2C4.3%2C-4.3%2C135%2C180%29%29%2C+locate%28.6%2C1.5%2C45%5Eo%29%2Clocate%2810.1%2C1.2%2C45%5Eo%29%2Clocate%28.1%2C11.2%2C45%5Eo%29%2C%0D%0Alocate%280%2C0%2CC%29%2Clocate%2812%2C0%2CB%29%2Clocate%28-.2%2C12.8%2CA%29%2C%0D%0Alocate%284.1%2C8.7%2CP%29%2C+locate%289.1%2C3.5%2CQ%29%0D%0A%0D%0A%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "Draw lines CR and RB so that ΔCRB ≅ ΔCPA\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%282800%2F9%2C400%2C-1%2C13%2C-5%2C13%2C%0D%0A%0D%0Aline%280%2C0%2C0%2C12%29%2C%0D%0Aline%280%2C0%2C4%2C8%29%2C%0D%0Aline%280%2C0%2C9%2C3%29%2C%0D%0Aline%280%2C0%2C12%29%2C%0D%0Aline%2812%2C0%2C0%2C12%29%2C%0D%0Alocate%28.6%2C1.5%2C45%5Eo%29%2Clocate%2810.1%2C1.2%2C45%5Eo%29%2Clocate%28.1%2C11.2%2C45%5Eo%29%2C%0D%0Ared%28arc%280%2C0%2C4.3%2C-4.3%2C18%2C63%29%2Carc%280%2C12%2C4.3%2C-4.3%2C270%2C315%29%2Carc%2812%2C0%2C4.3%2C-4.3%2C135%2C180%29%2C+arc%2812%2C0%2C4.6%2C-4.6%2C180%2C225%29%29%2C+%0D%0Alocate%280%2C0%2CC%29%2Clocate%2812%2C0%2CB%29%2Clocate%28-.2%2C12.8%2CA%29%2C%0D%0Alocate%284.1%2C8.7%2CP%29%2C+locate%289.1%2C3.5%2CQ%29%2C%0D%0Agreen%28line%280%2C0%2C8%2C-4%29%2Cline%288%2C-4%2C12%2C0%29%29%2Clocate%2810.1%2C0%2C45%5Eo%29%0D%0Alocate%288%2C-4%2CR%29%0D%0A%0D%0A%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r\n" );
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document.write( "Now draw in QR:\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%282800%2F9%2C400%2C-1%2C13%2C-5%2C13%2C%0D%0A%0D%0Aline%280%2C0%2C0%2C12%29%2C%0D%0Aline%280%2C0%2C4%2C8%29%2C%0D%0Aline%280%2C0%2C9%2C3%29%2C%0D%0Aline%280%2C0%2C12%29%2C%0D%0Aline%2812%2C0%2C0%2C12%29%2C%0D%0Alocate%28.6%2C1.5%2C45%5Eo%29%2Clocate%2810.1%2C1.2%2C45%5Eo%29%2Clocate%28.1%2C11.2%2C45%5Eo%29%2C%0D%0Ared%28arc%280%2C0%2C4.3%2C-4.3%2C18%2C63%29%2Carc%280%2C12%2C4.3%2C-4.3%2C270%2C315%29%2Carc%2812%2C0%2C4.3%2C-4.3%2C135%2C180%29%2C+arc%2812%2C0%2C4.6%2C-4.6%2C180%2C225%29%29%2C+%0D%0Alocate%280%2C0%2CC%29%2Clocate%2812%2C0%2CB%29%2Clocate%28-.2%2C12.8%2CA%29%2C%0D%0Alocate%284.1%2C8.7%2CP%29%2C+locate%289.1%2C3.5%2CQ%29%2C%0D%0Agreen%28line%280%2C0%2C8%2C-4%29%2Cline%288%2C-4%2C12%2C0%29%29%2Clocate%2810.1%2C0%2C45%5Eo%29%0D%0Alocate%288%2C-4%2CR%29%2Cblue%28line%289%2C3%2C8%2C-4%29%29%0D%0A%0D%0A%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r\n" );
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document.write( "You can finish now.  It's mostly corresponding parts of\r\n" );
document.write( "congruent triangles and the Pythagorean theorem.  Here are \r\n" );
document.write( "some of the steps:\r\n" );
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document.write( "ΔCRB ≅ ΔCPA\r\n" );
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document.write( "BR = AP\r\n" );
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document.write( "∠ACP = ∠BCR  \r\n" );
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document.write( "∠ACP + ∠PCQ + ∠QCB = 90°\r\n" );
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document.write( "∠ACP + 45° + ∠QCB = 90°\r\n" );
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document.write( "∠ACP + ∠QCB = 45°\r\n" );
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document.write( "∠BCR + ∠QCB = 45°\r\n" );
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document.write( "Show that  ΔQCP ≅ ΔQCR\r\n" );
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document.write( "Then PQ = QR\r\n" );
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document.write( "≅QBR is a right triangle\r\n" );
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document.write( "BR² + BQ² = QR²\r\n" );
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document.write( "AP² + BQ² = PQ²\r\n" );
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document.write( "If you have trouble finishing, tell me in the space below,\r\n" );
document.write( "and I'll get back to you be email.  (No charge, ever!!)\r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
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