$ \text{Step 1: Given Data} $

Truss with vertical loads:
\begin{array}{c}
W_A = 2\,{\rm{kN}} \\
W_H = 5\,{\rm{kN}} \\
W_G = 5\,{\rm{kN}} \\
W_F = 5\,{\rm{kN}} \\
W_E = 2\,{\rm{kN}}
\end{array}

Key dimensions:
\begin{array}{c}
AB = 2\,{\rm{m}} \\
BC = 2\,{\rm{m}} \\
CD = 2\,{\rm{m}} \\
DE = 2\,{\rm{m}} \\
CG = 3\,{\rm{m}} \\
AC = 4\,{\rm{m}} \\
AD = 6\,{\rm{m}} \\
AE = 8\,{\rm{m}}
\end{array}

$ \text{Step 2: Free Body Diagram} $

Reaction forces:
\begin{array}{c}
A_x = 0\,{\rm{kN}} \\
A_y = \text{To be determined} \\
E_y = \text{To be determined}
\end{array}

$ \text{Step 3: Reaction at E} $

Moment equilibrium about A:
\begin{array}{c}
\sum M_A = 0 \\
E_y \times 8 = 2 \times 8 + 5 \times 6 + 5 \times 4 + 5 \times 2 \\
E_y \times 8 = 16 + 30 + 20 + 10 \\
\hline
E_y = \frac{76}{8} = 9.5\,{\rm{kN}}
\end{array}

$ \text{Step 4: Section Analysis} $

Consider section FED with members:
\begin{array}{c}
F_{GF} = \text{Force in GF} \\
F_{GD} = \text{Force in GD} \\
F_{CD} = \text{Force in CD}
\end{array}

$ \text{Step 5: Angle Calculation} $

Angle θ between GC and CE:
\begin{array}{c}
\tan \theta = \frac{3}{4} \\
\theta = \tan^{-1}\left(\frac{3}{4}\right) \\
\hline
\theta \approx 37^\circ
\end{array}

$ \text{Step 6: Force in CD} $

Moment equilibrium about G:
\begin{array}{c}
\sum M_G = 0 \\
9.5 \times 4 – 2 \times 4 – 5 \times 2 – F_{CD} \times 3 = 0 \\
38 – 8 – 10 = 3F_{CD} \\
\hline
F_{CD} = \frac{20}{3} \approx 6.67\,{\rm{kN}}\,(\rm{T})
\end{array}

$ \text{Step 7: Length FD} $

Geometric similarity:
\begin{array}{c}
\frac{GC}{CE} = \frac{FD}{DE} \\
\frac{3}{4} = \frac{FD}{2} \\
\hline
FD = 1.5\,{\rm{m}}
\end{array}

$ \text{Step 8: Force in GF} $

Moment equilibrium about D:
\begin{array}{c}
\sum M_D = 0 \\
9.5 \times 2 – 2 \times 2 + F_{GF} \cos37^\circ \times 1.5 = 0 \\
19 – 4 = -1.197F_{GF} \\
\hline
F_{GF} = \frac{-15}{1.197} \approx -12.5\,{\rm{kN}}\,(\rm{C})
\end{array}

$ \text{Step 9: Joint C Analysis} $

Vertical equilibrium:

\begin{array}{c}
\sum F_y = 0 \\
F_{GC} = 0\,{\rm{kN}}\,(\text{Zero Force})
\end{array}

$ \text{Step 10: Results Summary} $

\begin{array}{c}
\text{CD: } 6.67\,{\rm{kN}}\,(\rm{T}) \\
\text{GF: } 12.5\,{\rm{kN}}\,(\rm{C}) \\
\text{GC: } 0\,{\rm{kN}}\,(\text{Inactive})
\end{array}

$ \text{Step 11: Verification} $

\begin{array}{c}
\text{Moment Check: } \sum M_A = 0 \quad \checkmark \\
\text{Force Balance: } \sum F_y = 0 \quad \checkmark \\
\hline
\text{All equilibrium conditions are satisfied}
\end{array}