document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1017250>Question 1017250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> http://prntscr.com/9xsn9a <BR>\n" );
document.write( "The answers are parallelogram, rectangle, square, and rhombus. <BR>\n" );
document.write( "The correct answer is rhombus, but I'm confused how? <BR>\n" );
document.write( "I plugged the diagonals into the slope formula and my final result when I multiplied the products of the slopes was 0/0 each time. <BR>\n" );
document.write( "Z (-4,2)<BR>\n" );
document.write( "W(1,5)<BR>\n" );
document.write( "X(5,2)<BR>\n" );
document.write( "Y(1,-1)\r<BR>\n" );
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document.write( "I got 0/9 for 2-2 over 5--4 which results in 0/9. <BR>\n" );
document.write( "I got -6/0 for -1-5 over 1-1 which results in -6/0 and then I multiplied 0/9 and -6/0 which gave me 0/0, but for the parallelogram to be a rhombus the product of the slopes has to be -1 and I got 0/0. So, I'm not sure why the correct answer is a rhombus. By the way, I got parallelogram for my answer.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #633577 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=633577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the slope of a horizontal line is 0.<BR>\n" );
document.write( "the slope of a vertical line is undefined.\r<BR>\n" );
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document.write( "the rule that the lines are perpendicular to each other when the product of the slopes is equal to -1 only works when both slopes are defined.\r<BR>\n" );
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document.write( "in the case of a horizontal line and a vertical line, that rule can't be used.\r<BR>\n" );
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document.write( "the rule that can still be used is that the slope of a line perpendicular to another line must be a negative reciprocal of the slope of that line.\r<BR>\n" );
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document.write( "the slope of the horizontal line is 0.\r<BR>\n" );
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document.write( "the negative reciprocal of 0 is -1 / 0 which is undefined.\r<BR>\n" );
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document.write( "since the slope of the vertical line is undefined, it must be perpendicular to the horizontal line.\r<BR>\n" );
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document.write( "here's a proof that the parallelogram is a rhombus if the diagonals are perpendicular.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.algebra.com/algebra/homework/Geometry-proofs/Geometry_proofs.faq.question.392003.html\" target = \"_blank\">http://www.algebra.com/algebra/homework/Geometry-proofs/Geometry_proofs.faq.question.392003.html</a>\r<BR>\n" );
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document.write( "they did not say, however, that the figure in the graph was a parallelogram.\r<BR>\n" );
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document.write( "the proof depends on the figure being a parallelogram.\r<BR>\n" );
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document.write( "you are just shown the graph.\r<BR>\n" );
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document.write( "the properties of a rhombus are:\r<BR>\n" );
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document.write( "the diagonals are perpendicular.<BR>\n" );
document.write( "the figure is a parallelogram.\r<BR>\n" );
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document.write( "to show the figure is a parallelogram, you have to show that the opposite sides are parallel and are congruent.\r<BR>\n" );
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document.write( "once you've shown that, you can then say that it must be a rhombus because, on top of that, the diagonals are perpendicular.\r<BR>\n" );
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document.write( "but, if you showed the opposite sides are parallel and that all the sides are congruent, then you've satisfied the definition of a rhombus.\r<BR>\n" );
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document.write( "also, in a parallelogram, the diagonals bisect each other.\r<BR>\n" );
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document.write( "that is not necessarily true in a quadrilateral, unless the quadrilateral is a parallelogram.\r<BR>\n" );
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document.write( "so, besides the fact that you struggled with the diagonals being perpendicular to each other, i think you have to show that the opposite sides are parallel (use their slopes), and that the opposite sides are congruent.\r<BR>\n" );
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document.write( "that says it's a parallelogram.\r<BR>\n" );
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document.write( "then, either all 4 sides are congruent to each other, which you would probably find after you measured all their lengths.\r<BR>\n" );
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document.write( "once you've done that, you don't need to state that the diagonals are perpendicular, although that would be icing on the cake.\r<BR>\n" );
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document.write( "before you can prove it's a rhombus, you have to prove it's a parallelogram, because a rhombus is a special kind of parallelogram.\r<BR>\n" );
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document.write( "here's a definition of a rhombus from wikipedia at <a  rel=nofollow HREF= \"https://en.wikipedia.org/wiki/Rhombus\" target = \"_blank\">https://en.wikipedia.org/wiki/Rhombus</a>\r<BR>\n" );
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document.write( "A simple (non self-intersecting) quadrilateral is a rhombus if and only if it is any one of the following:[6][7]\r<BR>\n" );
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document.write( "    a quadrilateral with four sides of equal length (by definition)<BR>\n" );
document.write( "    a quadrilateral in which the diagonals are perpendicular and bisect each other<BR>\n" );
document.write( "    a quadrilateral in which each diagonal bisects two opposite interior angles<BR>\n" );
document.write( "    a parallelogram in which a diagonal bisects an interior angle<BR>\n" );
document.write( "    a parallelogram in which at least two consecutive sides are equal in length<BR>\n" );
document.write( "    a parallelogram in which the diagonals are perpendicular (an orthodiagonal parallelogram)\r<BR>\n" );
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document.write( "any one of these definition defines a rhombus.\r<BR>\n" );
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