document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159413>Question 159413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PROVE:<BR>\n" );
document.write( "If an isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.<BR>\n" );
document.write( "GIVEN: triangle ABC is isosceles; line CD is the altitude to base of line AB<BR>\n" );
document.write( "TO PROVE: line CD bisects angle ACB<BR>\n" );
document.write( "Problem says that I have to come up with a plan of the proof as well.\r<BR>\n" );
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document.write( "HEEELP!!<BR>\n" );
document.write( "TIA, Joanne </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117575 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=117575\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your plan is as follows:<BR>\n" );
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document.write( "prove that CD is perpendicular to AB.<BR>\n" );
document.write( "prove that angles opposite congruent sides of isosceles triangle are congruent.  assume this is previously proven. if not, you'll have to prove it yourself.  i'll provide that proof separately.<BR>\n" );
document.write( "prove that the two right triangles created by the altitude are congruent.<BR>\n" );
document.write( "prove that angles created by altitude are equal to each other.<BR>\n" );
document.write( "prove that they bisect the angle.<BR>\n" );
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document.write( "proof that angles opposite congruent sides of isosceles triangle are congruent<BR>\n" );
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document.write( "triangle ABC is isosceles and AC = CB (given)<BR>\n" );
document.write( "draw CD to intersect AB so that AD = DB (construction)<BR>\n" );
document.write( "triangle ADC congruent to triangle BDC by SSS (AC = CB is given, CD = CD by reflexive property of equality (anything is equal to itself), AD = DB by construction)<BR>\n" );
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document.write( "your main proof.<BR>\n" );
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document.write( "CD is perpendicular to AD (this is by definition of the altitude of a triangle)<BR>\n" );
document.write( "***<BR>\n" );
document.write( "angle CAD congruent to angle CBD (opposite angles of an isosceles triangle are equal).  just stating it should be enough but if they want proof, it is up above.<BR>\n" );
document.write( "***<BR>\n" );
document.write( "triangle CDA is congruent to CDB (SSA - two triangle are congruent if two corresponding sides and an angle not between them are congruent.  this is a basic postulate of congruent triangles.  corresponding sides are CA congruent to CB, CD congruent to CD, corresponding angles are CAD congruent to CBD)<BR>\n" );
document.write( "***<BR>\n" );
document.write( "angle ACD = angle BCD (corresponding angles of congruent triangles are congruent)<BR>\n" );
document.write( "***<BR>\n" );
document.write( "CD bisects angle ACB (by definition the bisector of an angle creates two equal angles formed by the bisector)<BR>\n" );
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