Geometry

Question Analysis:
This question involves the properties of diagonals in a parallelogram.
The main focus is on using algebraic expressions to test whether the diagonals bisect each other, which is a defining property of a parallelogram.

Key Concept Explanation:
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
That means:
The two parts of diagonal AC (i.e., AE and EC) must be equal:
AE = EC
The two parts of diagonal BD (i.e., BE and ED) must be equal:
BE = ED
If both conditions are satisfied for the same value of x, then ABCD is a parallelogram.

Step-by-Step Solution:
AE = EC:
→ 2x + 3 = 5x − 9
→−3x = −12
→ x = 4
BE = ED:
→x + 6 = 3x − 2
→2x = 8
→x = 4

Common Mistakes:
Only checking one diagonal instead o...