document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185643>Question 1185643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello! Could you please help my child with these questions? Would appreciate if could please include an explanation for each answer. \r<BR>\n" );
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document.write( "Please determine if the statements below are ALWAYS , SOMETIMES or NEVER True. Please justify your answer.\r<BR>\n" );
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document.write( "If AB≅BC in ΔABC, then ∠BAC≅∠ABC.Always, sometimes, never?\r<BR>\n" );
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document.write( "If ∠BAC≅∠ABC in ΔABC, then AB≅BC. Always, sometimes, never?\r<BR>\n" );
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document.write( "CPCTC can be used as a reason in a proof for proving triangles congruent. Always, sometimes, never?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816484 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Hello! Could you please help my child with these questions? Would appreciate if could please include an explanation for each answer.<BR>\n" );
document.write( "Please determine if the statements below are ALWAYS , SOMETIMES or NEVER True. Please justify your answer.<BR>\n" );
document.write( "If AB≅BC in ΔABC, then ∠BAC≅∠ABC.Always, sometimes, never?<BR>\n" );
document.write( "If ∠BAC≅∠ABC in ΔABC, then AB≅BC. Always, sometimes, never?<BR>\n" );
document.write( "CPCTC can be used as a reason in a proof for proving triangles congruent. Always, sometimes, never?<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "(1)  If AB≅BC in ΔABC, then ∠BAC≅∠ABC. Always, sometimes, never?\r\n" );
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document.write( "     If AB≅BC in ΔABC,  it means that AB and BC are lateral sides of the isosceles triangle ABC\r\n" );
document.write( "     with the vertex B opposite to the base side.\r\n" );
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document.write( "     In this situation, the Geometry theorem states that the base angles A and C are congruent.\r\n" );
document.write( "     But the question asks about congruency of the OTHER pair of angles, namely A and B.\r\n" );
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document.write( "     These two angles, A and B, are not necessary congruent. \r\n" );
document.write( "     Under given condition, they are congruent ONLY for a particular case of the EQUILATERAL triangle.\r\n" );
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document.write( "     THEREFORE, the ONLY answer to this question is \"SOMETIMES\".\r\n" );
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document.write( "(2)  If ∠BAC≅∠ABC in ΔABC, then AB≅BC. Always, sometimes, never?\r\n" );
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document.write( "     If ∠BAC≅∠ABC in ΔABC,  it means that A and B are the base angles in the isosceles triangle ABC,\r\n" );
document.write( "     whose lateral sides are AC and AB.  Then the Geometry theorem states that the lateral sides AC and BC are congruent.\r\n" );
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document.write( "     But the question asks about congruency of different pair of sides, namely AB and BC.  \r\n" );
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document.write( "     These sides are not necessary congruent.\r\n" );
document.write( "     Under the given conditions, they are congruent ONLY for a particular case of the EQUILATERAL triangle.\r\n" );
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document.write( "     THEREFORE, the ONLY answer to this question is \"SOMETIMES\".\r\n" );
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document.write( "(3)  CPCTC can be used as a reason in a proof for proving triangles congruent. Always, sometimes, never?\r\n" );
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document.write( "     CPCTC is this logical statement  \"If two triangles are congruent, then their corresponding sides are congruent\".\r\n" );
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document.write( "     The posed question asks if CPCTC can be used in the proof of congruency triangles, i.e. opposite statement.\r\n" );
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document.write( "     The answer is \"NEVER\".\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "Please let me know if the son does understand my solution.\r<BR>\n" );
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