Geometry

Question Analysis:
Use distance formula to check congruence of opposite sides in the coordinate plane.

Key Concept Explanation:
Use distance formula to check whether both opposite sides are equal in length.

Step-by-Step Solution:
Calculate AB and CD:
AB = √[(5–1)² + (4–2)²] = √(16 + 4) = √20
CD = √[(7–3)² + (0–(–2))²] = √(16 + 4) = √20 → AB ≅ CD
AD = √[(3–1)² + (–2–2)²] = √(4 + 16) = √20
BC = √[(7–5)² + (0–4)²] = √(4 + 16) = √20 → AD ≅ BC
→ Both pairs of opposite sides congruent ⇒ Parallelogram