document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081439>Question 1081439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Thank you for your help in advance.\r<BR>\n" );
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document.write( "Prove the opposite angles of a parallelogram are congruent.<BR>\n" );
document.write( "Prove the base angles of an isosceles triangle are congruent.<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 #695489 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=695489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Start with the following isosceles triangle. The two equal sides are shown with one red mark and the angles opposites to these sides are also shown in red.\r<BR>\n" );
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document.write( "The strategy is to draw the perpendicular bisector from vertex <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > to segment <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB ALIGN=MIDDLE  ALT=\"AB\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Then use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SAS ALIGN=MIDDLE  ALT=\"SAS\"   DISABLED_style= \"max-width:90%; height:auto;\" > postulate to show that the two triangles formed are congruent.\r<BR>\n" );
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document.write( "If the two triangles are congruent, then corresponding angles to will be congruent.\r<BR>\n" );
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document.write( "Draw the perpendicular bisector from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > is bisected,we got\r<BR>\n" );
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document.write( "angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > which are same measure; so,  angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=+y ALIGN=MIDDLE  ALT=\"+x=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Segment <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC+=++BC ALIGN=MIDDLE  ALT=\"AC+=++BC\"   DISABLED_style= \"max-width:90%; height:auto;\" >... ( This one was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=given ALIGN=MIDDLE  ALT=\"given\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Segment <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CF+=+CF+ ALIGN=MIDDLE  ALT=\"CF+=+CF+\"   DISABLED_style= \"max-width:90%; height:auto;\" >(Common side is the same for both triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ACF ALIGN=MIDDLE  ALT=\"ACF\"   DISABLED_style= \"max-width:90%; height:auto;\" > and triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BCF ALIGN=MIDDLE  ALT=\"BCF\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Triangles <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ACF ALIGN=MIDDLE  ALT=\"ACF\"   DISABLED_style= \"max-width:90%; height:auto;\" > and triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BCF ALIGN=MIDDLE  ALT=\"BCF\"   DISABLED_style= \"max-width:90%; height:auto;\" > are then congruent by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SAS ALIGN=MIDDLE  ALT=\"SAS\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=side-angle-side ALIGN=MIDDLE  ALT=\"side-angle-side\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "In other words, by\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC ALIGN=MIDDLE  ALT=\"AC\"   DISABLED_style= \"max-width:90%; height:auto;\" >-angle(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >)-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CF ALIGN=MIDDLE  ALT=\"CF\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC ALIGN=MIDDLE  ALT=\"BC\"   DISABLED_style= \"max-width:90%; height:auto;\" >-angle(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >)-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CF ALIGN=MIDDLE  ALT=\"CF\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ACF ALIGN=MIDDLE  ALT=\"ACF\"   DISABLED_style= \"max-width:90%; height:auto;\" > and triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BCF ALIGN=MIDDLE  ALT=\"BCF\"   DISABLED_style= \"max-width:90%; height:auto;\" > are congruent, angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > = angle<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+B ALIGN=MIDDLE  ALT=\"+B\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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