Ratio of sides in a triangle vs ratio of angles? Given a triangle with the ratio of sides being $X: Y : Z$, is it true that the ratio of angles is also $X: Y: Z$?  Could I see a proof of this?  Thanks

No, it is not true. Consider a 45-45-90 right triangle:

(image from Wikipedia)
The sides are in the ratio $1:1:\sqrt{2}$, while the angles are in the ratio $1:1:2$.
