Geometry Similar Triangles
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How Similar
Similar Triangles

 

 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

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