Let’s analyze the problem step by step and solve it.

The problem requires proving $EF \parallel AD$. Here's how to complete the proof based on the given diagram and statements:

Proof:

1. $\angle DGA + \angle BAC = 180^\circ$ (Given).

   Since $AB \parallel CD$ (assumed), $\angle 1 = \angle 3$ by alternate interior angles.
   Reason: Alternate interior angles are equal when two lines are parallel.

2. $\angle 1 = \angle 2$ (Given).

   From the transitive property, $\angle 2 = \angle 3$.
   Reason: Transitive property of angle equality.

3. $EF \parallel AD$.

   Since $\angle 2 = \angle 3$, the lines $EF$ and $AD$ are parallel by the corresponding angles postulate.
   Reason: Corresponding angles are equal when two lines are parallel.

Complete Statements for the Table:

1. $\angle DGA + \angle BAC = 180^\circ$ (Given).
2. $AB \parallel CD$ $\Rightarrow \angle 1 = \angle 3$ (Alternate interior angles).
3. $\angle 1 = \angle 2$ (Given).
4. $\angle 2 = \angle 3$ (Transitive property of equality).
5. $EF \parallel AD$ (Corresponding angles postulate).

Would you like me to explain any step further or assist with related problems? Here are 5 questions to deepen understanding:

1. Why does the transitive property apply in step 4 of the proof?
2. How do alternate interior angles help prove parallel lines?
3. What is the role of corresponding angles in determining parallelism?
4. How does the relationship $\angle DGA + \angle BAC = 180^\circ$ influence the proof?
5. Can this method be applied to other triangle configurations?

Tip: Always check for parallel lines using angle relationships like alternate interior or corresponding angles!