document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201873>Question 201873</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Have a triangle (JKL) with J as point of triangle with a line going down to line K L and the point on the line where it meets is M .the angles created at M  are right angles. The given is that angle KJM is equal to angle LJM and line JM bisects line KL. How do I write a 2 column proof for tringle JKL as an isosceles.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152137 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=152137\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If I understand you correctly, your givens are:<BR>\n" );
document.write( "1.  angle JMK and angle JML are right angles.<BR>\n" );
document.write( "2.  angle KJM is congruent to angle LJM<BR>\n" );
document.write( "3.  line JM bisects line KL.<BR>\n" );
document.write( "start of note 1:<BR>\n" );
document.write( "I drew triangle KJL with K on the lower left, J on top, and L on the lower right.<BR>\n" );
document.write( "end of note 1:<BR>\n" );
document.write( "from this you want to prove that triangle KJL is an isosceles triangle.<BR>\n" );
document.write( "first you want to prove that triangle KJM and triangle LJM are congruent.<BR>\n" );
document.write( "this would lead to angle JKM and angle JLM being equal.<BR>\n" );
document.write( "in the proof below, the statement is in the left hand column and the reason is in the right hand column (in parentheses)<BR>\n" );
document.write( "start of example 1:<BR>\n" );
document.write( "1.  i will prove this for you (i think i know how).<BR>\n" );
document.write( "the statement above is i will prove this for you which is in the left hand column.  the reason is i think i know how which is shown in parentheses which means it will be in the right hand column.<BR>\n" );
document.write( "end of example 1:<BR>\n" );
document.write( "start of proof:<BR>\n" );
document.write( "1.  angle KMJ and angle LMJ are right angles (given).<BR>\n" );
document.write( "2.  angle KMJ is congruent to angle LMJ (all right angles are congruent).<BR>\n" );
document.write( "3.  segment JM bisects segment KL at M (given).<BR>\n" );
document.write( "4.  segment KM is congruent to ML (segment bisector creates 2 congruent segments).<BR>\n" );
document.write( "5.  triangle KJM is congruent to triangle LJM (SAS).<BR>\n" );
document.write( "start of note for 5:<BR>\n" );
document.write( "the congruent segments are JM to JM and KM to ML<BR>\n" );
document.write( "the congruent angle between them is angle KMJ to angle LMJ<BR>\n" );
document.write( "end of note for 5:<BR>\n" );
document.write( "6.  angle MKJ congruent to angle MLJ (corresponding angles of congruent triangles are congruent).<BR>\n" );
document.write( "7.  triangle KJL is an isosceles triangle (if 2 corresponding angles of a triangle are congruent, then the triangle is isosceles).<BR>\n" );
document.write( "end of proof:<BR>\n" );
document.write( "start of note 2:<BR>\n" );
document.write( "since you stated that segment JM bisects segment KL at a right angle, I did not need the fact that angle KJM is congruent to angle LJM because I had enough to prove triangles KJM and LJM were congruent without it.<BR>\n" );
document.write( "end of note 2: </SPAN>\n" );
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