ΔHFG is dilated by a scale factor of 2 with the center of dilation at point F. Then, it is reflected over line a to create ΔEFI. Based on these transformations, which statement is true?
Line segments EG and HI intersect at point F, forming triangles EFI and HFG. Line a intersects with both triangles at point F.
segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI
segment FG = segment FI, segment FH = segment FE, and segment HG = segment EI; ΔHFG ~ ΔEFI
segment FG = one half segment FE, segment FH = one half segment FI, and segment HG = one halfsegment EI; ΔHFG ~ ΔIFE
segment FG = segment FE, segment FH = segment FI and segment HG = segment EI; ΔHFG ~ ΔIFE
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.