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Answer:
yes
Step-by-step explanation:
If GH║FE, then ∆DEF ~ ∆DHG.
In similar triangles, corresponding sides have the same ratios.
The ratios of corresponding sides are ...
DG/DF = DH/DE
DG/(DG + GF) = 18/(18+36)
(1/2GF)/((1/2GF +GF) = 1/3
(1/2)/(3/2) = 1/3
1/3 = 1/3
Corresponding sides are proportional. Angle D is congruent to itself, so ∆DEF ~ ∆DHG by the SAS similarity postulate. Angles DGH and DFE are therefore congruent and GH║FE.
