In triangle MPK, on the continuation of the median ME, sharpening E is the segment ED equal

In triangle MPK, on the continuation of the median ME, sharpening E is the segment ED equal to ME. Prove that MPDK is a parallelogram.

By condition, ME = DE, point E is the middle of the RK, then PE = KE.

In triangles PME and DKE, angle PEM = DEK as vertical angles at the intersection of MD and PK, then triangles PME and DKE are equal on two sides and the angle between them, which means PM = DK.

Similarly, the triangles PED and MEK are equal in two sides and the angle between them, then PD = MK.

In the MPDK quadrangle the opposite sides are pairwise parallel, then the MPDK is a parallelogram, which is what we had to prove.