Given: ∠abc ≅ ∠def and ∠def less than∠ghi prove: ∠abc less than ∠ghi

This is actually more about relations between numbers than between angles: if , whatever is true for x must be true for y as well.

So, if and we know that , then as well: how could two identical objects not share the same properties?

In your case, you know that angles ABC and DEF are the same, and so whatever is true for DEF is true for ABC as well. If DEF is less than GHI, then ABC must be less than GHI as well.