



Say you
have a triangle like this one ...












Put it
into a copy machine 


that
makes things twice as big 


and you
get this ... 











The sides
got twice as long, 


but the
angles didn't change. 





In the
little triangle the side on the bottom 


is 2.4
times as long as the side on the left. 





In the
big triangle the side on the bottom 


is 2.4
times as long as the side on the left. 





If you
have a couple of these copies 


of
different sizes, math types would call them 





SIMILAR
TRIANGLES






We said
that no matter how big or small the triangle was 


the side
on the bottom is always 2.4 times as long 


as the
side on the left. 


In math
talk, we could say ... 











But
there's even more than that. 


On any of
the triangle copies of any size 


any side
divided by any other side 


will give
the same answer as you get 


when you
divide the same sides 


in any
other of the triangles. 





Example: 








This may
seem kind of dumb, but it really isn't. 


With this
trick and the Pythagorean theorem, 


math
types invented all of trigonometry. 





We used a
right triangle in this example, 


but
there's no rule that says you have to. 





This
trick works on any triangle. 





copyright 2005 Bruce Kirkpatrick 
