MHB Why do similar triangles have equal ratios of sides?

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I was wondering why similar triangles have the property that the ratios of the similar sides are equal.
Or why the triangular functions (sin, cos,...) for a certain angle is fixed.
They are related, and if I can find one of them, the other can be proved easily.
I was thinking about the slope of the straight line since it is fixed and it is equal to the tan(angle which the line made with the positive x-axis) .

Any ideas?

Thanks.
 
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... You can just prove buy saying that angle AB,for example, is equal to AB2
 
Amer said:
I was wondering why similar triangles have the property that the ratios of the similar sides are equal.

Hi Amer, :)

Refer either of the following links.

1) Equiangular Triangles are Similar - ProofWiki

2) http://farside.ph.utexas.edu/euclid/Elements.pdf (Page 160)
 

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