ΔEFI is dilated by a scale factor of one half with the center of dilation at point F. Then, it is reflected over line a to create ΔHFG. 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 FH = two segment FE, segment FG = two segment FI, and segment HG = two segment EI; ΔEFI ~ ΔHFG
two segment FH = segment FE, two segment FG = segment FI, and two segment HG = segment EI; ΔEFI ~ ΔHFG
segment FH = two segment FI, segment FG = two segment FE, and segment HG = two segment EI; ΔEFI ~ ΔGFH
two segment FH = segment FI, two segment FG = segment FE, and two segment HG = segment EI; ΔEFI ~ ΔGFH

It is given that ΔEFI is dilated by a scale factor of one half with the center of dilation at point F. Then, it is reflected over line a to create ΔHFG.

[tex]\overline{FH}=\frac{1}{2}\times \overline{FE}[/tex]

Multiply both sides by 2.

[tex]2\overline {FH}=\overline{FE}[/tex]

Similarly,

[tex]\overline{FG}=\frac{1}{2}\times \overline{FI}[/tex]

Multiply both sides by 2.

[tex]2\overline {FG}=\overline{FI}[/tex]

And,

[tex]\overline{HG}=\frac{1}{2}\times \overline{EI}[/tex]

Multiply both sides by 2.

[tex]2\overline {HG}=\overline{EI}[/tex]

By SSS property of similarity,

ΔEFI ~ ΔGFH

Since, [tex]2\overline {FH}=\overline{FE}[/tex], [tex]2\overline {FG}=\overline{FI}[/tex], [tex]2\overline {HG}=\overline{EI}[/tex], therefore ΔEFI ~ ΔGFH.

Therefore, the correct option is B.