Geometry

Question Analysis:
This question tests the ability to apply coordinate geometry to verify parallelogram properties.

Key Concept Explanation:
A quadrilateral is a parallelogram if both pairs of opposite sides are congruent (equal in length).

Step-by-Step Solution:
Calculate distances:
AB = √[(4-1)² + (4-2)²] = √(9+4) = √13
CD = √[(2-5)² + (-1-1)²] = √(9+4) = √13
BC = √[(5-4)² + (1-4)²] = √(1+9) = √10
AD = √[(2-1)² + (-1-2)²] = √(1+9) = √10
Since AB = CD and BC = AD, opposite sides are equal.

Option Analysis:
A: Correct - Demonstrates both pairs of opposite sides equal
B: Insufficient - Only shows one pair of sides parallel
C: Unnecessary - Angl...