document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147590>Question 147590</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An isosceles trapezoid must have two pairs of equal adjacent angles. State and prove the converse. \r<BR>\n" );
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document.write( "I know what the converse is, but i dont know how to prove it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108433 by </B><A HREF=/tutors/aboutme.mpl?userid=orca><B>orca(409)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=orca><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=108433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The converse theorem can be stated as:<BR>\n" );
document.write( "A quadrilateral is an isosceles trapezoid if it has two pairs of equal adjacent angles\r<BR>\n" );
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document.write( "PROOF<BR>\n" );
document.write( "In quadrilateral ABCD, <BR>\n" );
document.write( "< A = < B = a, < C = < D = b\r<BR>\n" );
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document.write( "As the sum of all the interior angles of a quadrilateral is 360 degrees, we have<BR>\n" );
document.write( "< A + < B + < C + < D = 360<BR>\n" );
document.write( "a + a + b + b = 360<BR>\n" );
document.write( "2a + 2b = 360<BR>\n" );
document.write( "a + b = 180\r<BR>\n" );
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document.write( "Thus < A + < D = 180<BR>\n" );
document.write( "AB and CD are parallel.\r<BR>\n" );
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document.write( "Next we need to prove that AD = BC<BR>\n" );
document.write( "Through A draw a line AE parallel to BC.<BR>\n" );
document.write( "As quadrilateral ABCE is a parallelogram, AE = BC ........(1)<BR>\n" );
document.write( "Since AE parallel to BC, < AED = < C.<BR>\n" );
document.write( "Thus triangle ADE is an isosceles triangle<BR>\n" );
document.write( "So AD = AE ........(2)<BR>\n" );
document.write( "From (1) and (2), we have<BR>\n" );
document.write( "AD = BC\r<BR>\n" );
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document.write( "So quadrilateral ABCD is an isosceles trapezoid.<BR>\n" );
document.write( " </SPAN>\n" );
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