Geometry

Question Analysis:
This question combines coordinate geometry with parallelogram proof techniques, testing understanding of how to apply the diagonal bisection property in a coordinate system.

Key Concept Explanation:
A quadrilateral is a parallelogram if and only if its diagonals bisect each other.
In coordinate geometry, this means the midpoints of both diagonals must be identical.

Step-by-Step Solution:
Calculate midpoint of AC: ((0 + 8)/2, (0 + 4)/2) = (4, 2)
Calculate midpoint of BD: ((3 + 5)/2, (4 + 0)/2) = (4, 2)
Since midpoints coincide, diagonals bisect each other → ABCD is a parallelogram.

Option Analysis:
Option A correctly applies the bisection criterion.
Option B (equal length) would prove isosceles trapezoid.
Opti...