document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=485935>Question 485935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what are the kinds of trapezoid and other kinds of a kite? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #332292 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=332292\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Trapezoids\r<BR>\n" );
document.write( "\n" );
document.write( "Definition: A trapezoid is a quadrilateral with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=exactly ALIGN=MIDDLE  ALT=\"exactly\"   DISABLED_style= \"max-width:90%; height:auto;\" > one pair of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallel ALIGN=MIDDLE  ALT=\"parallel\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The segment that connects the midpoints of the legs of a trapezoid is called the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mid-segment ALIGN=MIDDLE  ALT=\"mid-segment\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This segment’s length is always equal to one-half the sum of the trapezoid’s bases, or\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "mid-segment  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28base1%2Bbase2%29%2F2=%28a%2Bb%29%2F2 ALIGN=MIDDLE  ALT=\"m=%28base1%2Bbase2%29%2F2=%28a%2Bb%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It follows that the area of a trapezoid is equal to the length of this mid-segment multiplied by the height:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=mh ALIGN=MIDDLE  ALT=\"A=mh\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so, the area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a trapezoid is given by\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28%28a%2Bb%29%2F2%29h ALIGN=MIDDLE  ALT=\"A=%28%28a%2Bb%29%2F2%29h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Isosceles Trapezoids\r<BR>\n" );
document.write( "\n" );
document.write( "Definition: An <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=isosceles ALIGN=MIDDLE  ALT=\"isosceles\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=trapezoid ALIGN=MIDDLE  ALT=\"trapezoid\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a trapezoid whose legs are congruent.\r<BR>\n" );
document.write( "\n" );
document.write( "There are several theorems we can use to help us prove that a trapezoid is isosceles. These properties are listed below.\r<BR>\n" );
document.write( "\n" );
document.write( "(1) A trapezoid is isosceles if and only if the base angles are congruent.\r<BR>\n" );
document.write( "\n" );
document.write( "(2) A trapezoid is isosceles if and only if the diagonals are congruent.\r<BR>\n" );
document.write( "\n" );
document.write( "(3) If a trapezoid is isosceles, then its opposite angles are supplementary.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Kites or deltoids\r<BR>\n" );
document.write( "\n" );
document.write( "Definition: A <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kite+ ALIGN=MIDDLE  ALT=\"kite+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is a quadrilateral with two distinct pairs of adjacent sides that are congruent.\r<BR>\n" );
document.write( "\n" );
document.write( "Recall that parallelograms also had pairs of congruent sides. However, their congruent sides were always opposite sides. Kites have two pairs of congruent sides that meet at two different points.\r<BR>\n" );
document.write( "\n" );
document.write( "Kites have a couple of properties that will help us identify them from other quadrilaterals.\r<BR>\n" );
document.write( "\n" );
document.write( "(1) The diagonals of a kite meet at a right angle.\r<BR>\n" );
document.write( "\n" );
document.write( "(2) Kites have exactly one pair of opposite angles that are congruent.\r<BR>\n" );
document.write( "\n" );
document.write( "Is a trapezoid a kite?\r<BR>\n" );
document.write( "\n" );
document.write( "answer is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=No ALIGN=MIDDLE  ALT=\"No\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "In general, a trapezoid is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-sided ALIGN=MIDDLE  ALT=\"4-sided\"   DISABLED_style= \"max-width:90%; height:auto;\" > figure with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=one ALIGN=MIDDLE  ALT=\"one\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pair ALIGN=MIDDLE  ALT=\"pair\"   DISABLED_style= \"max-width:90%; height:auto;\" > of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallel ALIGN=MIDDLE  ALT=\"parallel\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides. \r<BR>\n" );
document.write( "\n" );
document.write( "The kite is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-sided ALIGN=MIDDLE  ALT=\"4-sided\"   DISABLED_style= \"max-width:90%; height:auto;\" > figure with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=two ALIGN=MIDDLE  ALT=\"two\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pairs ALIGN=MIDDLE  ALT=\"pairs\"   DISABLED_style= \"max-width:90%; height:auto;\" > of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=directly ALIGN=MIDDLE  ALT=\"directly\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=connected ALIGN=MIDDLE  ALT=\"connected\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=equilateral ALIGN=MIDDLE  ALT=\"equilateral\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sides ALIGN=MIDDLE  ALT=\"sides\"   DISABLED_style= \"max-width:90%; height:auto;\" >, each pair being of different length. \r<BR>\n" );
document.write( "\n" );
document.write( "You can picture the kite by picturing the \"traditional\" kind of kite that flies. It is an \"enlongated diamond\" with the lower pair of sides longer than the top pair. Nowhere in the formula for a kite is there a provision for any two sides to be parallel. There cannot be. So a trapezoid, which has a pair of parallel sides, can't be a kite.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );