Median AD of triangle ABC is extended beyond point D to a segment, DE, equal to AD

Median AD of triangle ABC is extended beyond point D to a segment, DE, equal to AD, point E is connected to point C. Prove that triangle ABC is equal to triangle ECD.

Since, according to the condition, the segment AD is the median of the triangle ABC, then the segment BD = CD.

By condition, AD = ED.

Consider triangles ABD and ECD, in which the angle ADB = EDC as the vertical angles at the intersection of straight lines AE and BC.

Then the triangles ABD and ECD are equal in two sides and the angle between them – the first sign of the equality of triangles, which was required to be proved.