document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010962>Question 1010962</A>: <I><SPAN STYLE=\"word-break: break-all;\"> prove the following parallelograms is not rectangle? C(-9,4) D(-4,8) E(2,6)F (-3,2) ?\r<BR>\n" );
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document.write( "Prove that A PARALLELOGRAM WITH VERTICES T(-2,3) E(-5,-4) A(2,-1) M (5,6) is a rhombus but not a square\r<BR>\n" );
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document.write( "Prove that R(2,1) E (10,7) C(7,11) T (-1,5) are the vertices of a rectangle but not a square\r<BR>\n" );
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document.write( "Prove that M(-2,1) A(1,6) T(8,3) H (5,-4) are the vertices of a square    I really need the help   please! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #626615 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=626615\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume that you have followed the labeling convention of starting with the lower left point and then proceed clockwise.<BR>\n" );
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document.write( "1)  a rectangle has two pairs of equal sides and four 90 degree interior angles<BR>\n" );
document.write( "the sides are CD, DE, EF, FC<BR>\n" );
document.write( "note that the diagonals bisect the interior angles<BR>\n" );
document.write( "CD = sqrt((-4-(-9))^2 + (8-4)^2) = 6.403124237<BR>\n" );
document.write( "DE = sqrt((2-(-4))^2 + (6-8)^2) = 6.32455532<BR>\n" );
document.write( "EF = sqrt((-3-2)^2 + (2-6)^2) = 6.403124237<BR>\n" );
document.write( "FC = sqrt((-9-(-3))^2 + (4-2)^2) = 6.32455532<BR>\n" );
document.write( "side CD = EF and side DE = FC<BR>\n" );
document.write( "the adjacent sides of a rectangle are perpendicular to each other which means that the slopes of adjacent sides must be the negative reciprocal of each other<BR>\n" );
document.write( "slope of FC = (2-4) / (-3-(-9) = -2 / 6 = -1/3<BR>\n" );
document.write( "slope of CD = (8-4) / (-9-(-4)) = 4 / -5 = -4/5  <BR>\n" );
document.write( "therefore CDEF is not a rectangle<BR>\n" );
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document.write( "2) note that all squares are rhombus but not all rhombus are squares <BR>\n" );
document.write( "a square has all four sides equal and four 90 degree interior angles<BR>\n" );
document.write( "TE = sqrt((-5-(-2))^2 + (-4-3)^2) = 7.615773106<BR>\n" );
document.write( "EA = sqrt((2-(-5))^2 + (-1-(-4)^2) = 7.615773106<BR>\n" );
document.write( "AM = sqrt((5-2)^2 + (6-(-1))^2) = 7.615773106<BR>\n" );
document.write( "MT = sqrt((5-(-2))^2 + (6-3)^2) = 7.615773106<BR>\n" );
document.write( "side TE=EA=AM=MT<BR>\n" );
document.write( "the diagonals of a rhombus are perpendicular to each other and bisect each other<BR>\n" );
document.write( "let X be the point of intersection of the diagonals<BR>\n" );
document.write( "TA = sqrt((2-(-2))^2 +  (-1-3)^2) = 5.656854249<BR>\n" );
document.write( "EM = sqrt((5-(-5))^2 +  (6-(-4))^2) = 11.180339887<BR>\n" );
document.write( "sin of angle XEA = (TA/2) / EA = 0.371390676<BR>\n" );
document.write( "inverse sin of 0.371390676 = 21.801409465 degrees<BR>\n" );
document.write( "angle XEA = 21.801409465<BR>\n" );
document.write( "now angle TEA = 2 * 21.801409465 = 43.602818929 degrees<BR>\n" );
document.write( "TEAM is a rhombus but not a square<BR>\n" );
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document.write( "3) RE = sqrt((10-2)^2 + (7-1)^2) = 10<BR>\n" );
document.write( "EC = sqrt((7-10)^2 + (11-7)^2) = 5<BR>\n" );
document.write( "CT = sqrt((-1-7)^2 + (5-11)^2) = 10<BR>\n" );
document.write( "TR = sqrt((-1-2)^2 + (5-1)^2 = 5<BR>\n" );
document.write( "side RE=CT and EC=TR<BR>\n" );
document.write( "RECT is not a square<BR>\n" );
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document.write( "4) MA = sqrt((1-(-2))^2 + (6-1)^2) = sqrt(34)<BR>\n" );
document.write( "AT = sqrt((8-1)^2 + (3-6)^2) = sqrt(58)<BR>\n" );
document.write( "TH = sqrt((5-8)^2 + (-4-3)^2) = sqrt(58)<BR>\n" );
document.write( "HM = sqrt((5-(-2))^2 + (-4-1)^2) = sqrt(74)<BR>\n" );
document.write( "the coordinates are not correct for a square<BR>\n" );
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document.write( " </SPAN>\n" );
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