Let #ABCD# be a trapezoid with lower base #AD# and upper base #BC#. Connect vertex #B# with midpoint #N# of opposite leg #CD# and extend it beyond point #N# to intersect with continuation of lower base #AD# at point #X#. Consider two triangles #Delta BCN# and #Delta NDX#. They are congruent by angle-side-angle theorem because Therefore, segments #BC# and #DX# are congruent, as well as segments #BN# and #NX#, which implies that #N# is a midpoint of segment #BX#. But #AX# is a sum of lower base #AD# and segment #DX#, which is congruent to upper base #BC#. Therefore, #MN# is equal to half of sum of two bases #AD# and #BC#. End of proof. The lecture dedicated to this and other properties of quadrilaterals as well as many other topics are addressed by a course of advanced math for high school students at Unizor.
Answer: true Step-by-step explanation: A median of a trapezoid is the segment that joins the midpoints of the nonparallel sides (legs). Theorem: The median of a trapezoid is parallel to each base and the length of the median equals one-half the sum of the lengths of the two bases. |