Geometry

Question Analysis：
This proof-based question requires applying multiple angle properties to establish a parallelogram.

Key Concept Explanation：
Definitive parallelogram proofs require：
• Both pairs of opposite angles equal, OR
• Both pairs of adjacent angles supplementary

Step-by-Step Solution：
Given ∠E + ∠F = 180°, we know one pair of adjacent angles is supplementary
Given ∠F = ∠H establishes one pair of opposite angles equal
Combining these：
• ∠E = 180° - ∠F
• ∠G = 180° - ∠H = 180° - ∠F = ∠E
Thus we have：
• Both pairs of opposite angles equal (∠F=∠H and ∠E=∠G)
• Both pairs of adjacent angles supplementary

Option Analysis：
• A) Incorrect - The combination of conditions is sufficient
• B) Partial - Doesn't acknowledge adjacent angle condition
• C...