The segments MN and EF meet at their midpoint P. Prove that lines EN and MF are parallel.

Angle MOF = EPH as vertical angles at the intersection of straight lines MH and EF.

Point Р is the middle of the segments МН and ЕF, then the segment МР = НР, the segment ЕР = FP.

Then the triangles МФР and ЕНР are equal on two sides and the angle between them, the first sign of equality of triangles.

Since the triangles МФР and ЕНР are equal, the angle РМF = РНО, and since these are criss-crossing angles at the intersection of the lines ЕН and МF secant МН, the lines ЕН and МF are parallel, which was required to be proved.