Geometry

Question Analysis:
This question uses a diagram to test a student’s understanding of parallelogram conditions.
The main focus is applying the “one pair of opposite sides both parallel and congruent” rule.

Key Concept Explanation:
A quadrilateral is a parallelogram if one pair of opposite sides is both parallel and congruent.
We're told that PQ // SR, so we now check when PQ = SR.

Step-by-Step Solution:
Set PQ equal to SR: 2x + 1 = x + 5
Subtract x from both sides: x + 1 = 5
Subtract 1 from both sides: x = 4
x = 4 makes the two opposite sides congruent as well as parallel.

Common Mistakes:
Confusing parallelism alone with sufficiency for a parallelogram
Plugging in value...