Geometry

Question Analysis:
This coordinate geometry question checks for understanding of slope and distance relationships used to prove a parallelogram.
The main focus is using coordinate plane tools to apply a side-based condition.

Key Concept Explanation:
Equal slopes ⇒ parallel lines
Equal lengths ⇒ congruent sides
Therefore, if one pair of opposite sides is both parallel and congruent, then the figure is a parallelogram.

Step-by-Step Solution:
Slope of JK = slope of LM → JK ∥ LM
Length of JK = length of LM → JK ≅ LM
This satisfies the known parallelogram condition
Conclusion: JKLM is a parallelogram

Option Analysis:
A. A rhombus requires all four sides congruent
B. Trapezoid has only one pair of parallel sides – congruent length not needed
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