Final answer:
Without diagrams or additional context, proving EABC is a parallelogram is challenging; however, showing parallel and equal opposite sides, equal opposite angles, or bisected diagonals can help in such geometric proofs.
Step-by-step explanation:
The student is provided with several geometric facts involving midpoints, line segments, triangles, and collinearity, and is tasked with proving that quadrilateral EABC is a parallelogram. Without the provided diagrams or further context of points D, A, B, C, E, and F, it is challenging to offer a definitive proof. However, to demonstrate a quadrilateral is a parallelogram, one could show opposite sides are parallel and equal in length, opposite angles are equal, or that diagonals bisect each other. Specific geometric properties, such as midpoints and congruent segments, play a vital role in such proofs. As the information is currently insufficient to support a full answer, I encourage the student to provide additional context or a diagram for a complete proof.
If a parallelogram is the subject of the proof, investigating the properties related to midpoints and congruences, such as the Midpoint Theorem or properties of triangles, may be helpful.