How to prove that the median line of a triangle is parallel and equal to half of the third side, and can't be proved by similar triangles@@@@ Such as the title

Lengthen the median line so that the length of the extension line is equal to the length of the median line. Connecting the endpoint of the extension line with a vertex of the triangle (the side opposite to the median line) will form a quadrilateral (the quadrilateral with the side opposite to the median line and the side opposite to the extension line and the median line). It is proved that the quadrilateral is an equal quadrilateral
According to a set of opposite sides equal and equal proof

Complete the graph and write out the known and proving of the following proposition to complete the proving process. Proposition: the median line of the triangle is parallel to the third side and equal to half of the third side_ . verification:_ . certification:

Known: as shown in the figure, in △ ABC, points D and E are the midpoint of AB and AC respectively; Prove: de ‖ BC, de = 12bc. Prove: extend De to point F, make ef = De, connect CF. ∵ point E is the midpoint of AC, ∵ AE = EC. ∵ in △ AED and △ CEF, AE = EC ≌ AED = ≌ CEF = EF, ≌ AED ≌ CEF (SAS) ≌ ad = CF, ≌ a = ≌ ECF, ∥ ab ∥ CF. ∵ point D is the midpoint of AB, ∥ ad = BD. ∥ BD = CF. ∥ quadrilateral bdfc is parallelogram. ∥ de ‖ BC, DF = BC. ∥ de = 12df = 12bc

Verification: the median line of triangle is parallel to the third side and equal to half of the third side

It is known that De is the median line of △ ABC. Prove: De / / BC, de = 1 / 2 BC. Prove: extend De to F, make ef = De, connect CF ∵ (because) AE = CE, angle AED = angle CEF, ≌ ad = CF, angle ade = angle f ≌ BD / / CF ∵ ad = BD ≌ BD = CF ≌ quadrilateral BCFD is a parallelogram

How to prove that the median line of a triangle is parallel and equal to half of the third side, and can't be proved by similar triangles@@@@ Such as the title