document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935779>Question 935779</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I prove that the angle bisector of the vertex angle of an isosceles triangle is an altitude? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569198 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=569198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-1.5%2C8.5%2C%0D%0Agreen%28line%280%2C0%2C0%2C8%29%29%2C%0D%0Agreen%28arrow%280%2C8%2C0%2C-1.4%29%29%2C%0D%0Atriangle%28-4%2C0%2C4%2C0%2C0%2C8%29%2C%0D%0Alocate%28-0.1%2C8.5%2CO%29%2Clocate%280.1%2C0%2CB%29%2C%0D%0Alocate%28-4.1%2C0%2CA%29%2Clocate%283.9%2C0%2CC%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The angle bisector (ray OB) divides the vertex angle AOC into two congruent angles (angle AOB and angle COB).<BR>\n" );
document.write( "It also divides the triangle into two triangles (triangle AOB and triangle COB).<BR>\n" );
document.write( "You can prove that those two triangles are congruent.<BR>\n" );
document.write( "They have one pair of congruent angles (angle AOB and angle COB).<BR>\n" );
document.write( "Those angles are flanked by pairs of congruent sides,<BR>\n" );
document.write( "because side OA is congruent with side OC (by definition of isosceles triangle),<BR>\n" );
document.write( "and side OB is congruent with itself.<BR>\n" );
document.write( "So, by SAS congruency, triangle AOB and triangle COB are congruent.<BR>\n" );
document.write( "Then, by CPCTC (Congruent Parts of Congruent Triangles are Congruent),<BR>\n" );
document.write( "angle ABO and angle CBO are congruent,<BR>\n" );
document.write( "but since points A, B, and C are colinear,<BR>\n" );
document.write( "angles ABO and CBO being congruent means they are right angles.<BR>\n" );
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document.write( "Segment BO is the altitude of triangle ACO,<BR>\n" );
document.write( "because it is perpendicular to base AC,<BR>\n" );
document.write( "and goes from a point on line AC to vertex O. </SPAN>\n" );
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