In a trapezium AB

Construction: Join CF and extent it to cut AB at point M

Firstly, in triangle MFB and triangle DFC

DF = FB (As F is the mid-point of DB)

∠DFC = ∠MFB (Vertically opposite angle)

∠DFC = ∠FBM (Alternate interior angle)

∴ By ASA congruence rule

∆MFB ≅ DFC

Now, in triangle CAM

E and F are the mid-points of AC and CM respectively

∴ EF = 1/2 (AM)

EF = 1/2 (AB – MB)

EF = 1/2 (AB-CD)

Hence, option D is correct