document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=805916>Question 805916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HELP! The directions say that there is more information than is needed.  We are to state the one piece of information that is not needed then do a two column proof that does not use that information.<BR>\n" );
document.write( "Given: Segment LM is congruent to segment LN<BR>\n" );
document.write( "Segment KM is congruent to segment KN<BR>\n" );
document.write( " Ray KO bisects angle MKN<BR>\n" );
document.write( "Prove LO bisects angle MLN<BR>\n" );
document.write( "Thanks in advance! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #485609 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=485609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Unless more information is given in a figure, I do not see any superfluous, unneeded information.<BR>\n" );
document.write( "Maybe there was a figure that you could not include in your post.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If you remove the statement \"Segment LM is congruent to segment LN\",<BR>\n" );
document.write( "I do not even know that a point named L exists.<BR>\n" );
document.write( "If you remove the statement \"Segment KM is congruent to segment KN\",<BR>\n" );
document.write( "I do not even know that a point named N exists.<BR>\n" );
document.write( "If you remove the statement \"Ray KO bisects angle MKN\",<BR>\n" );
document.write( "I do not even know that a point named O exists.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If you tell me that there is a picture that shows a quadrilateral KLMN,<BR>\n" );
document.write( "such as the ones drawn in black below (or maybe a rotated version),<BR>\n" );
document.write( "with diagonals (or extended diagonals) like the ones drawn in green below,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-3%2C0%2C0%2C4%29%2Cline%283%2C0%2C0%2C4%29%2C%0D%0Aline%28-3%2C0%2C0%2C-4%29%2Cline%283%2C0%2C0%2C-4%29%2C%0D%0Agreen%28line%28-3%2C0%2C3%2C0%29%29%2Cgreen%28line%280%2C-4%2C0%2C4%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-3%2C7%2C%0D%0Aline%28-3%2C0%2C0%2C6%29%2Cline%283%2C0%2C0%2C6%29%2C%0D%0Aline%28-3%2C0%2C0%2C-2%29%2Cline%283%2C0%2C0%2C-2%29%2C%0D%0Agreen%28line%28-3%2C0%2C3%2C0%29%29%2Cgreen%28line%280%2C-2%2C0%2C6%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-9%2C1%2C%0D%0Aline%28-3%2C0%2C0%2C-2%29%2Cline%283%2C0%2C0%2C-2%29%2C%0D%0Aline%28-3%2C0%2C0%2C-8%29%2Cline%283%2C0%2C0%2C-8%29%2C%0D%0Agreen%28line%28-3%2C0%2C3%2C0%29%29%2Cgreen%28line%280%2C1%2C0%2C-8%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the intersection of the diagonals is point O,<BR>\n" );
document.write( "then \"Ray KO bisects angle MKN\" is not needed.<BR>\n" );
document.write( "In that case, you would know that triangles MKN and MLN<BR>\n" );
document.write( "are isosceles triangles, sharing side MN as their potentially unequal side.<BR>\n" );
document.write( "You could prove that those diagonals split the quadrilateral into congruent triangles, and they split each isosceles triangle into two congruent right triangles.<BR>\n" );
document.write( "That would prove<BR>\n" );
document.write( "\"Ray KO bisects angle MKN\" and<BR>\n" );
document.write( "\"Ray LO bisects angle MLN\",<BR>\n" );
document.write( "as least regarding the acute angles with those names.<BR>\n" );
document.write( "The constructions that are usually taught early in geometry class to to draw the bisector of an angle or the perpendicular bisector of a segment are all based on this.<BR>\n" );
document.write( "In a better world, all teachers that show that construction (from elemntary school to college) would explain what it's based on, and all students would know it. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );