If E and F are the mid-points of the two non-parallel sides AD and BC of the trapezium ABCD, in which AB ∥ CD, then find EF = ?
\[\frac{1}{2}(AB + CD)\]
In trapezium ABCD, AB and CD are the parallel sides and AD, BC are the non-parallel sides (legs). E and F are the midpoints of the legs.
By the mid-segment theorem for a trapezium, the segment joining the midpoints of the legs is parallel to the parallel sides and its length is the average of their lengths.
So \(EF = \dfrac{1}{2}(AB + CD)\).
Hence, \(\dfrac{1}{2}(AB + CD)\).
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