Answer
G
Work Step by Step
It is not F because the lengths could be the same, but they form a different shape with different angles.
It is not H because all of the angles could be the same, but the lengths could be different. Congruency is not the same thing as proportionality.
It is not I because the polygons could just be two different squares.
It is G because under those conditions, no matter what, the polygons would be congruent.