In isosceles ΔABC, point D is the midpoint of the base AC. Beams AB and CB outside ΔABC are marked with points M and N

In isosceles ΔABC, point D is the midpoint of the base AC. Beams AB and CB outside ΔABC are marked with points M and N, respectively, so that the angle BDM is equal to the angle BDN. Prove that ΔBDM = ΔBDN

Angles ABC and SVM are adjacent; angle CBM = 180-angle ABC
Angles ABC and ABN are adjacent; angle ABN = 180 – angle ABC
Then the angle СBN = ABN
Consider the triangles BDM and BDN:
1) Angle CBN = ABN
2) BD – general
3) angle BDM = BDN
The triangles are equal in side and two adjacent corners.