Geometry

Question Analysis:
This question tests the distinction between valid and invalid parallelogram criteria.
The main focus is to identify that both pairs of opposite sides must be congruent to prove a quadrilateral is a parallelogram.

Key Concept Explanation:
Valid criteria for parallelograms include:
Both pairs of opposite sides are congruent.
Both pairs of opposite sides are parallel.
One pair of sides is both parallel and congruent.
Invalid criteria (like those in A, B, D) do not meet these standards.

Step-by-Step Solution:
Recall the parallelogram theorems:
Option C directly matches the "both pairs of opposite sides congruent" theorem.
Eliminate invalid options:
A) One pair of congruent sides is insufficient (e.g., isosceles trapezoid).
B) Adjacent sides congruent describe a kite, not a parallelogram.
D) All sides different cannot form a parallelogram (needs at least two pair...