The correct statement is: segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI
This is because when a figure is dilated by a scale factor of 2 with the center of dilation at a point, all the corresponding sides are scaled by that factor. Additionally, when a figure is reflected over a line, the corresponding segments remain equal in length but may change direction.