document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=747238>Question 747238</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I really need help with the statement and reason of this problem.\r<BR>\n" );
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document.write( "Given: Line segment BD bisects angle ABC<BR>\n" );
document.write( "        Angle BAD is congruent to angle BCD<BR>\n" );
document.write( "Prove: Triangle ADC is isosceles\r<BR>\n" );
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document.write( "So far I have this:<BR>\n" );
document.write( "1. Line segment BD bisects angle ABC<BR>\n" );
document.write( "Reason: Given\r<BR>\n" );
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document.write( "2. Angle BAD is congruent to angle BCD<BR>\n" );
document.write( "Reason: Given\r<BR>\n" );
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document.write( "3. Line segment AB is congruent to line segment CB<BR>\n" );
document.write( "Reason ?\r<BR>\n" );
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document.write( "4.Triangle ABC is isosceles<BR>\n" );
document.write( "Reason: Def of isosceles triangle\r<BR>\n" );
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document.write( "5. Triangle ADC is isosceles<BR>\n" );
document.write( "Reason: Triangle ABC is isosceles which makes triangle ADC isosceles; Def of isosceles triangle \r<BR>\n" );
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document.write( "I am really unsure about this problem as it just does not see correct but I do not understand how to make it correct. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #454779 by </B><A HREF=/tutors/aboutme.mpl?userid=timvanswearingen><B>timvanswearingen(106)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=timvanswearingen><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=timvanswearingen><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=454779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I believe the reason you're looking for on step 3 is the isosceles triangle theorem.  \r<BR>\n" );
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document.write( "Since angle BAD is congruent to angle BCD, the sides opposite those angles in triangle ABC are congruent.  \r<BR>\n" );
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document.write( "Thus, AB is congruent to CB.  \r<BR>\n" );
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document.write( "Assuming this problem looks like a kite, after step 4,\r<BR>\n" );
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document.write( "5.  let E be the point of intersection between AC and BD. \r<BR>\n" );
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document.write( "6.  you need to show that triangle ABE is congruent to triangle CBE using ASA (angle side angle).  \r<BR>\n" );
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document.write( "7.  Then AE is congruent to CE by CPCTC. (corresponding parts of congruent triangles are congruent.)\r<BR>\n" );
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document.write( "8.  Also, angle AEB is congruent to angle CEB by CPCTC \r<BR>\n" );
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document.write( "9.  Angle CEB is congruent to angle AED and angle AEB is congruent to angle CED (vertical angles)\r<BR>\n" );
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document.write( "10.  Thus, angle AED is congruent to angle CED (transitive)\r<BR>\n" );
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document.write( "11.  ED is congruent to ED (reflexive)\r<BR>\n" );
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document.write( "12.  By SAS (side angle side) triangle AED is congruent to triangle CED.\r<BR>\n" );
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document.write( "13.  AD is congruent to CD by CPCTC.\r<BR>\n" );
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document.write( "14.  Thus, triangle ADC is isosceles by the definition of an isosceles triangle.<BR>\n" );
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