document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246288>Question 246288</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a confusing proof.  <BR>\n" );
document.write( "GIVEN: 1)triangle ABC is isosceles.<BR>\n" );
document.write( "       2)line segment BD is a median to base AC<BR>\n" );
document.write( "PROVE: line segment BD is also an altitude<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179900 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=179900\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Triangle is ABC.\r<BR>\n" );
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document.write( "AD intersects AC at D.\r<BR>\n" );
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document.write( "It's a median so it splits the line AC into 2 equal parts.\r<BR>\n" );
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document.write( "You have:\r<BR>\n" );
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document.write( "AB = BC (legs of isosoceles triangle)\r<BR>\n" );
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document.write( "AD = DC (median splits AC into 2 equal parts by definition)\r<BR>\n" );
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document.write( "BD = BD (identity - same line segment is equal to itself)\r<BR>\n" );
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document.write( "triangles ABD and DBC are congruent (sss)\r<BR>\n" );
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document.write( "angle ADB = angle CDB (corresponding angles of congruent triangles are equal).\r<BR>\n" );
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document.write( "angle ADB and CDB are supplementary (their sum is equal to 180 degrees because their outer line segments form a straight line).\r<BR>\n" );
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document.write( "angle ADB and angle CDB must each be 90 degrees (they are equal and their sum is equal to 180.).\r<BR>\n" );
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document.write( "angle ADB and angle CDB are right angles (right angle = 90 degrees).\r<BR>\n" );
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document.write( "BD is perpendicular to AC (intersects at a right angle therefore is perpendicular).\r<BR>\n" );
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document.write( "or something like that.\r<BR>\n" );
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document.write( "you prove the angles are congruent.\r<BR>\n" );
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document.write( "you prove the angles have to be right angles.\r<BR>\n" );
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document.write( "that proves that the median is also an altitude because an altitude is perpendicular to the base by definition.\r<BR>\n" );
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