How does a translation affect the properties of a two-dimensional figure?

So when you translate something in geometry, you're simply just moving it around. You're not dilating, rotating, or anything like that, just moving it. If you translate say a rectangle, it will remain a rectangle, just moved wherever you move it. This is similarly the same with an angle, the measure of the angle won't change. When doing proofs you're going to want to make sure and understand these properties of translations. 

Property 1: Line segments are taken to line segments of the same length 

Property 2: Angles are taken to angles of the same measure 

Property 3: Lines are taken to lines, and parallel lines are taken to parallel lines

I hope this helped you understand.