If is the midsegment of trapezoid then
Let be a trapezoid and be its midsegment.
Draw the line containing the base and the line passing through and Let be the intersection point between these two lines.
With the information written before and the Angle-Side-Angle Congruence Theorem, it can be concluded that The right-hand side relation above implies that is the midpoint of In consequence, is a midsegment of Thus, the Triangle Midsegment Theorem leads to the following conclusion. Because then is parallel to each base of the trapezoid. Using the Segment Addition Postulate can be rewritten as follows. Since then Finally, substituting the equation above into the equation given by the Triangle Midsegment Theorem, it will be obtained the desired result.