document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179586>Question 1179586</A>: <I><SPAN STYLE=\"word-break: break-all;\"> https://ibb.co/jgpq3pX (Please copy paste the link to view the figure)\r<BR>\n" );
document.write( "\n" );
document.write( "Given: AE = DE; EB = EC<BR>\n" );
document.write( "Prove: a. Triangle AEB = Triangle DEC<BR>\n" );
document.write( "       b. Triangle ABC = Triangle DCB </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850211 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Perfect, let's break down this geometric proof.\r<BR>\n" );
document.write( "\n" );
document.write( "**Given:**\r<BR>\n" );
document.write( "\n" );
document.write( "* AE = DE<BR>\n" );
document.write( "* EB = EC\r<BR>\n" );
document.write( "\n" );
document.write( "**Prove:**\r<BR>\n" );
document.write( "\n" );
document.write( "* a. △AEB ≅ △DEC<BR>\n" );
document.write( "* b. △ABC ≅ △DCB\r<BR>\n" );
document.write( "\n" );
document.write( "**Proof:**\r<BR>\n" );
document.write( "\n" );
document.write( "**a. △AEB ≅ △DEC**\r<BR>\n" );
document.write( "\n" );
document.write( "| Statement | Reason |<BR>\n" );
document.write( "|---|---|<BR>\n" );
document.write( "| 1. AE = DE | Given |<BR>\n" );
document.write( "| 2. EB = EC | Given |<BR>\n" );
document.write( "| 3. ∠AEB ≅ ∠DEC | Vertical angles are congruent |<BR>\n" );
document.write( "| 4. △AEB ≅ △DEC | Side-Angle-Side (SAS) Congruence Theorem (AE = DE, ∠AEB ≅ ∠DEC, EB = EC) |\r<BR>\n" );
document.write( "\n" );
document.write( "**b. △ABC ≅ △DCB**\r<BR>\n" );
document.write( "\n" );
document.write( "To prove this, we need to establish that AB = DC, AC = DB and BC is a shared side.\r<BR>\n" );
document.write( "\n" );
document.write( "| Statement | Reason |<BR>\n" );
document.write( "|---|---|<BR>\n" );
document.write( "| 1. AE = DE | Given |<BR>\n" );
document.write( "| 2. EB = EC | Given |<BR>\n" );
document.write( "| 3. △AEB ≅ △DEC | Proven in part a |<BR>\n" );
document.write( "| 4. AB = DC | Corresponding Parts of Congruent Triangles are Congruent (CPCTC) |<BR>\n" );
document.write( "| 5. AC = AE + EC | Segment Addition Postulate |<BR>\n" );
document.write( "| 6. DB = DE + EB | Segment Addition Postulate |<BR>\n" );
document.write( "| 7. AC = DE + EB | Substitution Property (substitute AE with DE and EC with EB) |<BR>\n" );
document.write( "| 8. AC = DB | Transitive Property of Equality (since AC = DE + EB and DB = DE + EB) |<BR>\n" );
document.write( "| 9. BC = BC | Reflexive Property of Equality (any segment is congruent to itself) |<BR>\n" );
document.write( "| 10. △ABC ≅ △DCB | Side-Side-Side (SSS) Congruence Theorem (AB = DC, AC = DB, BC = BC) |<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );