



A
trapezoid has two parallel sides



and two
not parallel sides. 











If we
draw another line inside the trapezoid 


half way
between the top and bottom lines. 











This line
will cut the sides on the left and right 


exactly
in half. 











Now try
this ... 


Draw a
line inside the trapezoid 


one third
of the way down from the top line 


to the
bottom line. 

















Because
1/3 is EXACTLY half as big as 2/3. 











Since the
side on the left 


and the
side on the right are not parallel, 


one can
be really long and the other can be really short. 


In any
case, the lengths on the left 


will
usually not be the same as the lengths on the right. 





Example: 


Find the
unknown lengths in the trapezoid. 











The two
pieces of the side on the left 


are the
same length as each other. 


That
means the two pieces on the right side 


are the
same length as each other. 


So the
unknown length is 5






Example: 


Find
the unknown length









The side
piece on the top left 


is half
as long as the side piece on the bottom left. 


That
means the unknown side piece on the top right 


is half
as long as the side piece on the bottom right. 


The
bottom right piece is 8 units long 


so the
unknown top right piece is 4 units long. 





The rule
we can use with these problems is: 











With this
little rule, we can figure out 


the
missing side piece of any trapezoid. 





Example: 


Find the
length of the unknown side piece ... 











Math
people LOVE to use "X" for values they don't know. 


Using X,
we can write ... 











We want
to get X all by itself. 


Multiply
both sides by ^{15}/1 ... 











Simplify
... 











copyright 2005 Bruce Kirkpatrick 
