In quadrilateral ABCD the point P is the midpoint of the side AB and the point Q is the midpoint of the opposite side CD. If AD = 10 cm and BC = 14 cm, which statement about the length of PQ is correct?

Write the segment PQ as a sum: going from P to Q equals half the journey A to D plus half the journey B to C. Hence PQ is at most ½(AD + BC) = ½(10 + 14) = 12 cm, and the two half-journeys line up — giving the maximum — exactly when AD and BC point the same way, that is when AD ∥ BC and ABCD is a trapezium. The fixed value 12 cm is the mid-segment result for a TRAPEZIUM only; it is a ceiling, not a guarantee, for a general quadrilateral. The values 2 cm and 24 cm come from differencing or adding the sides without halving.