Question 807536
<pre>
These two oblique triangles are similar (have the same shape):

{{{drawing(400,400,-.2,1.3,-.2,1.3,triangle(0,0,1,0,.7,1.1),
arc(0,0,.6,-.6,0,58),
arc(1,0,.6,-.6,105,180), arc(1,0,.5,-.5,105,180),
arc(1,0,.5,-.5,105,180), 
arc(.7,1.1,.5,-.5,239,286),
arc(.7,1.1,.4,-.4,239,286),
arc(.7,1.1,.6,-.6,239,286))}}}{{{drawing(200,200,-.2,1.3,-.2,1.3,triangle(0,0,1,0,.7,1.1),
arc(0,0,.6,-.6,0,58),
arc(1,0,.6,-.6,105,180), arc(1,0,.5,-.5,105,180),
arc(1,0,.5,-.5,105,180), 
arc(.7,1.1,.5,-.5,239,286),
arc(.7,1.1,.4,-.4,239,286),
arc(.7,1.1,.6,-.6,239,286))}}}  

They have the same three angles, but certainly not the same size sides.

So the answer is no, because any two similar triangles have the same 
three angles, yet the sides may be entirely different, as the above two
similar triangles show.

Edwin</pre>