Trapezium midpoints of diagonals:\nIn a trapezium with parallel sides 8 cm and 4 cm, M and N are the midpoints of the two diagonals. Find the length MN (in cm).

Introduction / Context:
There is a standard trapezium property: the segment joining the midpoints of the diagonals is parallel to the bases, and its length equals half the difference of the parallel sides’ lengths. This is frequently examined in geometry aptitude questions.

Given Data / Assumptions:

• Parallel sides (bases) are 8 cm and 4 cm.
• M and N are midpoints of the diagonals.

Concept / Approach:
Apply the property directly: MN = |base1 − base2| / 2. Since the segment is always parallel to the bases, orientation does not affect length—only the base lengths matter.

Step-by-Step Solution:

Verification / Alternative check:
Construct a coordinate model (e.g., bases on horizontal lines) and verify via midpoint calculations; the result matches the property.

Why Other Options Are Wrong:
6 and 12 mistake sum for difference; 1 cm halves the wrong quantity; only 2 cm matches the theorem exactly.

Common Pitfalls:
Confusing mid-segment between bases (which is the average of bases) with the midpoint-of-diagonals segment (which is half the difference).

Final Answer:
2 cm