Given MNP-isosceles MP base K midpoint MP ME = PF Prove that KN is the bisector of angle EKF.

Since the triangle МНР is isosceles, then the angle НМР = НРМ.

Point K, by condition, is the middle of the base MP, then MK = PK.

ME = PF by condition, then the triangles MEK and PFK are equal on two sides and the angle between them, then KE = KF.

In triangles KEN and KFN, the side KN is common, KE = KF, EH = FH since MH = PH, and ME = PF.

Then the triangles KEN and KFH are equal on three sides, which means that the angle KNE = KHF, and then KN is the bisector of the angle EKF, which was required to prove.