She didn't answer your questions, but just drew the triangles, but
didn't draw the line segments AA', BB', and CC'. But then, the lines 
would have been cluttered and hard to see.

Here is her second drawing, cropped,



Now I'll draw in the line segments AA', BB', CC' in red.

If you'll look carefully, you'll see they all look both parallel and
equal in length.

 

Let A = (p,q), B = (r,s), and C = (t,u). 

She picked p=0, q=0, r=0, s=4, t=5, u=0, but you can pick ANY numbers you 
like for them as long as they're different points:

A = (p,q), so A' = (p+4, q-3)
B = (r,s), so A' = (r+4, s-3)
C = (t,u), so A' = (t+4, u-3)







They all have the same slope, -3/4, which means that the three lines will be
parallel, regardless of what you choose for points (p,q), (r,s), and (t,u).

Not only that, but what about their lengths?







The lengths of those parallel lines are also the same, 5.

The two triangles ABC and A'B'C' are also necessarily congruent, right? Or
wrong?

Edwin