Geometry

Question Analysis:
This high-difficulty problem requires analyzing multiple geometric constraints.
The main focus is determining the most specific quadrilateral satisfying all conditions simultaneously.

Key Concept Explanation:
Condition 1 establishes it as a parallelogram
Condition 2 (perpendicular diagonals) suggests rhombus/square
Condition 3 (right angle) confirms rectangle properties
Condition 4 (angle bisector) is specific to rhombuses/squares
Only squares satisfy all parallelogram, rectangle, and rhombus properties

Step-by-Step Solution:
Parallel sides confirm parallelogram base
Perpendicular diagonals upgrade to rhombus classification
Right angle introduces rectangle properties
Angle bisector confirms equilateral angles
Square is the only quadrilateral satisfying all conditions

Option Analysis:
A. Insufficient - Fails condition 2 and 4
B. Insufficient - Fails condition 3
C. Correct - Satisfies ...