Trapezoid midsegment = (a + b) / 2 and parallel

Dependencies: Triangle midsegment theorem (Triangle midsegment theorem), Midsegment converse (Midsegment converse), transitivity of parallelism (Parallel is transitive).

Statement

Let $ABCD$ be a trapezoid with $AB \parallel CD$ ($AB$, $CD$ are the two bases) and $AD$, $BC$ the two legs. Let $E \in AD$ and $F \in BC$ be the midpoints of the legs; the segment $EF$ is the trapezoid midsegment. Then

In words, the trapezoid midsegment is parallel to the two bases and has length equal to half their sum.