document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85736>Question 85736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the locus of points in a plane equidistant from the sides of an angle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61940 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=61940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The locus of these points is the line that is the bisector of the angle.  To convince yourself <BR>\n" );
document.write( "of this, draw an angle and then bisect it. Next, pick any point on the angle bisector and <BR>\n" );
document.write( "from that point construct perpendiculars to the two sides of the angle. You can see that these<BR>\n" );
document.write( "perpendiculars are equal in length. This is not a rigorous proof of that but you can make<BR>\n" );
document.write( "it \"correct\" by noticing that the right angles, the bisected portions of the original <BR>\n" );
document.write( "angle, and the common side of the two triangles (the bisector) form a pair of congruent<BR>\n" );
document.write( "triangles.  Therefore, the length of the perpendiculars to each side of the bisector<BR>\n" );
document.write( "are congruent and, therefore, equal in length. Difficult to put into words, but if you play<BR>\n" );
document.write( "with it for a while you'll see how this works.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );