Answer:
The length of Segment GF is 120
Explanation:
Given that EH = 80, and AB, GF, RH, and DI are parallel lines, we have;
DC ≅ DE ≅ EF ≅ FA Given
Therefore, CI ≅ HI ≅HG ≅ GB (Triangle proportionality theorem)
From where we have;
EH/GF =CH/CG (Intercept theorem otherwise known as Thales' theorem )
CH = 2 × CI (Transitive property of equality)
Also CG = 3 × CI (Transitive property of equality)
EH/GF = 2×CI/(3×CI) = 2/3
EH/GF = 2/3
80/GF = 2/3
Therefore we have;
Segment GF = 80 × 3/2 = 120
The length of Segment GF = 120.