Answer:
The correct option is;
Segment FE over 3 = Segment FH
Segment FI over 3 = Segment FG, and
Segment EI over 3 = Segment HG
ΔEFI ~ ΔHFG
Step-by-step explanation:
The given transformations are'
ΔEFI is dilated by a scale factor of 1/3 and then it is reflected over line a
By dilation, we have
FH = 1/3×FE
FG = 1/3×FI
HG = 1/3×EI
Also by reflection over a line, the relative positions of the y-coordinates of the points remain the same while the x coordinates changes sign such that an upright mirror image of the dilated triangle is formed
Therefore, since we have;
the same for both triangles, that is given the following relation;
FG/FH = (1/3×FI)/(1/3×FE) = FI/FE
Then, ΔEFI is similar to ΔHFG (triangle similarity requirement AAA)
Hence, the correct option is that the
Segment FE over 3 = Segment FH
Segment FI over 3 = Segment FG, and
Segment EI over 3 = Segment HG
ΔEFI ~ ΔHFG.