In this image, you are asked to match each statement about a parallelogram $ABCD$ with the corresponding reason. Here are the matching statements and their reasons:

1. $\overline{AB} \parallel \overline{CD}, \overline{AD} \parallel \overline{CB}$: Definition of parallelogram
   Explanation: By definition, opposite sides of a parallelogram are parallel.

2. $\angle CDB \cong \angle ABD$: Alternate interior angles
   Explanation: When two lines are parallel, alternate interior angles are congruent.

3. $\overline{CD} \cong \overline{AB}$: Opposite sides of a parallelogram are congruent
   Explanation: In a parallelogram, opposite sides are always equal in length.

4. $\triangle ABD \cong \triangle CDB$: ASA (Angle-Side-Angle)
   Explanation: The two triangles are congruent by the Angle-Side-Angle (ASA) congruence criterion, using one pair of congruent angles (alternate interior angles), the congruent sides, and the included angle.

Let me know if you want more details or explanations!

Here are five related questions to expand your understanding:

1. What are the properties of diagonals in a parallelogram?
2. Can you prove that the diagonals of a parallelogram bisect each other?
3. How does the Alternate Interior Angles Theorem apply to parallel lines?
4. What other ways can you prove two triangles are congruent besides ASA?
5. How can you use the definition of a parallelogram to determine unknown angles or sides?

Tip: When working with parallelograms, always remember that both opposite sides and opposite angles are congruent, and the diagonals bisect each other.