document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622241>Question 622241</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I prove two triangles congruent in a quadrilateral? I already have two angles congruent, because it is in the given info. Also they gave me a pair of congruent lines, what's next? Is it another angle? Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #391238 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=391238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I can't see your figure, so I'll guess it's something like<BR>\n" );
document.write( "this.  You have a kite ABCD with a diagonal AC:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%283200%2F11%2C370%2C-1.5%2C2.5%2C-3.5%2C2%2Cgreen%28line%280%2C1.5%2C0%2C-3%29%29%2C%0D%0Alocate%28-.05%2C1.75%2CA%29%2Clocate%28-1.2%2C0.1%2CB%29%2Clocate%28-.05%2C-3%2CC%29%2Clocate%281.1%2C0.1%2CD%29%2C%0D%0Aline%28-1%2C0%2C0%2C1.5%29%2C+line%280%2C1.5%2C1%2C0%29%2C+line%281%2C0%2C0%2C-3%29%2Cline%280%2C-3%2C-1%2C0%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Given:   AB &#8773; AD<BR>\n" );
document.write( "       &#8736;ABC &#8773; &#8736;ADC<BR>\n" );
document.write( "Prove: &#5123;ABC &#8773; &#5123;ADC\r<BR>\n" );
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document.write( "I'll just give you an outline. You'll have to write the<BR>\n" );
document.write( "2-column proof.\r<BR>\n" );
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document.write( "Draw BD:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%283200%2F11%2C370%2C-1.5%2C2.5%2C-3.5%2C2%2Cgreen%28line%280%2C1.5%2C0%2C-3%29%29%2Cred%28line%28-1%2C0%2C1%2C0%29%29%2C%0D%0Alocate%28-.05%2C1.75%2CA%29%2Clocate%28-1.2%2C0.1%2CB%29%2Clocate%28-.05%2C-3%2CC%29%2Clocate%281.1%2C0.1%2CD%29%2C%0D%0Aline%28-1%2C0%2C0%2C1.5%29%2C+line%280%2C1.5%2C1%2C0%29%2C+line%281%2C0%2C0%2C-3%29%2Cline%280%2C-3%2C-1%2C0%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then &#5123;ABD is isosceles because its legs AB and AD are given congruent. Therefore <BR>\n" );
document.write( "base angles &#8736;ABD &#8773; &#8736;ADB.  Since we are given <BR>\n" );
document.write( "&#8736;ABC &#8773; &#8736;ADC, then m&#8736;ABD = m&#8736;ADC.  Since &#8736;ABD &#8773; &#8736;ADB, m&#8736;ABD = m&#8736;ADB.  <BR>\n" );
document.write( "Subtracting equals from equals, we get that m&#8736;CBD = m&#8736;CDB and &#8736;CBD &#8773; &#8736;CDB.<BR>\n" );
document.write( "Therefore &#5123;BCD is isosceles because its base angles are congruent.<BR>\n" );
document.write( "BC &#8773; DC because they are legs of isosceles &#5123;BCD.  Now we have <BR>\n" );
document.write( "AB &#8773; AD, &#8736;ABC &#8773; &#8736;ADC, BC &#8773; DC.   Then &#5123;ABC &#8773; &#5123;ADC by SAS.\r<BR>\n" );
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document.write( "Edwin</pre>  </SPAN>\n" );
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