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 #117557 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=117557\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Draw the isosceles triangle. Then draw the altitude. <BR>\n" );
document.write( "That is what you are \"given\"\r<BR>\n" );
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document.write( "You also know that two angles of the isosceles triangle are equal. Let the two equal angles in the original isosceles triangle be A. \r<BR>\n" );
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document.write( "Euclid tells us that every triangle has 180 degrees of interior angle in it.<BR>\n" );
document.write( "So the third angle in the isosceles triangle is (180-2A)\r<BR>\n" );
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document.write( "By definition, an altitude forms a right angle with the base it intersects.<BR>\n" );
document.write( "Thus there are 2 right angles formed at the foot of the altitude.\r<BR>\n" );
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document.write( "So, you can now show that the two angles formed at the vertex where the altitude was dropped from must be equal (each being 180-90-A) = 90-A\r<BR>\n" );
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document.write( "(90-A) = 1/2(180-2A)<BR>\n" );
document.write( "Thus the two new angles are equal, and are 1/2 the size of the original one. So the original angle is bisected by the altitude.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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