document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147478>Question 147478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given square ABCD, let P and Q be the points outside the square that make triangles CDP and BCQ equilateral. Prove that triangle APQ is also equilateral. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108438 by </B><A HREF=/tutors/aboutme.mpl?userid=orca><B>orca(409)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=orca><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=108438\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> PROOF \r<BR>\n" );
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document.write( "To prove triangle APQ is equilateral, we need to show that AP = AQ = PQ.\r<BR>\n" );
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document.write( "Next we will show that triangles ABQ, ADP and CPQ are congruent.<BR>\n" );
document.write( "< ADP = 90 + 60 = 150<BR>\n" );
document.write( "< ABQ = 90 + 60 = 150<BR>\n" );
document.write( "< PCQ = 360 - 90 - 60 - 60 = 150<BR>\n" );
document.write( "So < ADP = < ABQ = < PCQ\r<BR>\n" );
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document.write( "AB = AD = CP<BR>\n" );
document.write( "BQ = DP = CQ\r<BR>\n" );
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document.write( "So triangles ABQ, ADP and CPQ are congruent.\r<BR>\n" );
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document.write( "Thus AP = AQ = PQ<BR>\n" );
document.write( " </SPAN>\n" );
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