document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1073145>Question 1073145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that parallelogram is a rhombus if its diagonals bisect at right angles <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688008 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=688008\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The diagonals of a parallelogram bisect each other,<BR>\n" );
document.write( "splitting the parallelogram into 4 triangles.<BR>\n" );
document.write( "If they intersect at right angles,<BR>\n" );
document.write( "those 4 triangles are right triangles.<BR>\n" );
document.write( "If the length of the diagonals are D and d,<BR>\n" );
document.write( "All 4 of those right triangles have legs of length <BR>\n" );
document.write( "D/2 and d/2.<BR>\n" );
document.write( "With a pair of congruent sides flanking congruent right angles,<BR>\n" );
document.write( "they are congruent right triangles,<BR>\n" );
document.write( "and their corresponding other sides (hypotenuses)<BR>\n" );
document.write( "are also congruent.<BR>\n" );
document.write( "So, the 4 sides of the parallelogram (the 4 hypotenuses)<BR>\n" );
document.write( "are congruent, and a parallelogram with 4 congruent sides<BR>\n" );
document.write( "is called a rhombus.<BR>\n" );
document.write( "(It could even be the particular type of rhombus that we call a square). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );