Hi Mellie,
It is always great to see you on the forum :)
Prove or explain why three reflections can transform a figure onto another figure if they are congruent
I don't have a great explanation here but maybe I can do so pictures to help you think one up for yourself - or someone else might weigh it.
I just realized that this is only 2 reflections. Did it have to be three or could it be 3 or less??
Never mind, I have already inserted the first triangle pic so I might as well talk about it.
1) I started with the brown triangle on the right and wanted to reflect it across to the brown triangle on the left.
2) I drew a perpendicular bisector between two corresponding vertices A and A'.
3) Then I reflected the triangle on the right across this line, resulting in the yellow triangle.
4) Then I drew another perpendicular bisector between 2 corresponding vertices. C' and C''. This will always go through A.
5) Then I reflected the yellow triangle across this line and that puts me in the position of the initial second triangle 
Ok, now I will go think, and play, some more. :D
