document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167637>Question 167637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given: Triangle MLP is isosceles, N is the midpoint of MP<BR>\n" );
document.write( "Prove: LN is perpendicular to MP \r<BR>\n" );
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document.write( "2 column chart \r<BR>\n" );
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document.write( "so far i have done <BR>\n" );
document.write( "Triangle MLP is isoscele - Given<BR>\n" );
document.write( "ML is congruent to PL- Def. of isosceles triangle<BR>\n" );
document.write( "N is the midpoint of MP- Given<BR>\n" );
document.write( "MN is congruent to PN- Def. of midpoint<BR>\n" );
document.write( "Angle LNM is congruent to Angle LNP- Linear Pair angles are congruent<BR>\n" );
document.write( "Triangle LNM is congruent to Triangle LPN- SAS \r<BR>\n" );
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document.write( "im not sure if this is right plus i have to find the result  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123532 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=123532\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given: Triangle MLP is isosceles, N is the midpoint of MP<BR>\n" );
document.write( "Prove: LN is perpendicular to MP<BR>\n" );
document.write( "2 column chart<BR>\n" );
document.write( "so far i have done<BR>\n" );
document.write( "Triangle MLP is isoscele - Given<BR>\n" );
document.write( "ML is congruent to PL- Def. of isosceles triangle<BR>\n" );
document.write( "N is the midpoint of MP- Given<BR>\n" );
document.write( "MN is congruent to PN- Def. of midpoint<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Angle LNM is congruent to Angle LNP- Linear Pair angles are congruent<BR>\n" );
document.write( "THIS SHOULD BE:<BR>\n" );
document.write( "angle LMN = angle LPN - if 2 sides of a triangle are congruent, then the angles opposite those sides are congruent also.<BR>\n" );
document.write( "i believe you were referring to the base angles of the isosceles triangle, and not the angles formed at the midpoint of MP.<BR>\n" );
document.write( "base angles of the triangle are LMN and LPN.<BR>\n" );
document.write( "angles formed at the midpoint are LNM and LNP.<BR>\n" );
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document.write( "Triangle LNM is congruent to Triangle LPN- SAS<BR>\n" );
document.write( "THIS IS OK.<BR>\n" );
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document.write( "now that you have that triangle LMN congruent to triangle LPN, you can prove that angle LNM congruent to angle LNP.<BR>\n" );
document.write( "reason:<BR>\n" );
document.write( "corresponding angles of congruent triangles are congruent.<BR>\n" );
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document.write( "then you can show that angle LNM is supplementary to angle LNP.<BR>\n" );
document.write( "reason:<BR>\n" );
document.write( "if the exterior sides of two adjacent angles form a straight line, then the angles are supplementary.<BR>\n" );
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document.write( "then you can show that angle LNM + angle LNP = 180 degrees.<BR>\n" );
document.write( "reason:<BR>\n" );
document.write( "if 2 adjacent angles are supplementary, then the sum of their angles is 180 degrees.<BR>\n" );
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document.write( "then you can show that angle LNM and angle LNP are each equal 90 degrees.<BR>\n" );
document.write( "reason:<BR>\n" );
document.write( "angle LNM + angle LNP = 180 degrees.<BR>\n" );
document.write( "this is the same as 2 * angle LNM = 180 degrees (substitution of equals)<BR>\n" );
document.write( "this means angle LNM = 180 / 2 = 90 degrees (algebra)<BR>\n" );
document.write( "this means that angle LNP = 90 degrees (equal to angle LNM).<BR>\n" );
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document.write( "then you can show that LN is perpendicular to MP<BR>\n" );
document.write( "reason:<BR>\n" );
document.write( "2 lines intersecting at 90 degrees angle are perpendicular to each other.<BR>\n" );
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document.write( " </SPAN>\n" );
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