Prove that if the side and the height and median of one triangle drawn to it are, respectively, equal to the side and the height

Prove that if the side and the height and median of one triangle drawn to it are, respectively, equal to the side and the height and median of the other triangle drawn to it, then such triangles are equal.

Given:
Triangle ABC and triangle A1B1C1
АL and А1L1 – medians of triangles.
Angle BLA = angle B1L1A1
AL = A1L1
BC = B1C1
Prove:
That these two triangles are equal.

Decision:
Consider triangles АLC and А1L1С1
AL = A1L1 (by condition)
Angle СLA = C1L1A1 (by condition)
Therefore, triangle ALC = triangle A1L1C1
And angle ALB = angle A1L1C1.

Consider triangles ALB and A1L1B1
Angle ALB = Angle A1L1B1
BL = B1L1 (by condition)
AL = A1L1 (by condition)
Hence, triangle ALB = triangle AA1L1B1.

Consider triangles ABC and A1B1C1
BC = B1C1 (conditional)
AC = A1C1
AB = A1B1
So these two triangles are equal.