Trapezoid Midsegment

Analysis 1
In the previous geometric construction, vertices E and F are midpoints. Change the position of vertices B or C. Observe the measurements of segments BC, AD and EF. Can you notice some relation between the measurement of segment EF and the other two segments?
Property 1
If a line segment joins the midpoints of the non-parallel sides of a trapezoid, then: [list][*]It is parallel to the bases; [/*][*]It is equal to one half the sum of the bases.[/*][/list]
Proof
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Information: Trapezoid Midsegment