document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255998>Question 255998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given:<BR>\n" );
document.write( " angle 1 is congruent to angle 2\r<BR>\n" );
document.write( "\n" );
document.write( "prove:<BR>\n" );
document.write( "  tiangle JOE is isosceles\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(please really need help.. i'm bad in geometry..) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188166 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=188166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> triangle is JOE.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "J is on top.<BR>\n" );
document.write( "O is bottom left.<BR>\n" );
document.write( "E is bottom right.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "angle 1 is angle JOE.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the angle on the bottom left corner of the triangle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "angle 2 is angle JEO.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the angle on the bottom right corner of the triangle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "drop a perpendicular from J to intersect with the line OE at point L.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "line JL is perpendicular to line OE at L.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means that angle JLO is 90 degrees and angle JLE is also 90 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have formed 2 right triangles.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they are triangle JLO and triangle JLE.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "These triangles are congruent by AAS.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "AAS means 2 corresponding angles and the non-included side.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The angles that are congruent are JOE and JEO and JLO and JLE.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The non-included sides that are congruent are JL and JL.   Since this line is part of both triangles, then it is congruent to itself.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the triangles are congruent, then their corresponding sides are congruent.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This means that side JO is congruent to side JE.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your original triangle is JOE.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "JOE is an isosceles triangle because it has 2 sides that are congruent to each other.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "proof is done.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "triangle we used in this proof is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "\r\n" );
document.write( "                                     J\r\n" );
document.write( "                                     x\r\n" );
document.write( "                                   x x x\r\n" );
document.write( "                                 x   x   x\r\n" );
document.write( "                               x     x     x\r\n" );
document.write( "                             x       x       x\r\n" );
document.write( "                           x         x         x\r\n" );
document.write( "                         x           x           x\r\n" );
document.write( "                       x             x             x\r\n" );
document.write( "                     x               x               x\r\n" );
document.write( "                   x                 x                 x\r\n" );
document.write( "                 x                   x                   x\r\n" );
document.write( "               x    1           3    x   4            2    x\r\n" );
document.write( "           O x x x x x x x x x x x x x x x x x x x x x x x x x E\r\n" );
document.write( "                                     L  \r\n" );
document.write( "</PRE><BR>\n" );
document.write( "angle JOE is the same as angle 1.<BR>\n" );
document.write( "angle JEO is the same as angle 2.<BR>\n" );
document.write( "angle JLO is the same as angle 3.<BR>\n" );
document.write( "angle JLE is the same as angle 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "note that angle JOE is the same as angle JOL is the same as angle 1.<BR>\n" );
document.write( "note that angle JEO is the same as angle JEL is the same as angle 2. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );