It is known that ad is the height on the waist of an isosceles triangle, and the degree of vertex angle is 0

It is known that ad is the height on the waist of an isosceles triangle, and the degree of vertex angle is 0

If ad intersects the line segment of BC: Yes (angle B is the vertex angle)
Because the angle DAB is 60 degrees and ad is perpendicular to BC, the angle ADB is 90 degrees,
The angle abd = 90-60 = 30 degrees, that is, the vertex angle = 30 degrees
If ad intersects the extension line of BC: Yes (angle B is the vertex angle)
Because the angle DAB is 60 degrees and ad is perpendicular to BC, the angle ADB is 90 degrees,
The angle DBA is 30 degrees, the vertex angle is 180-30 = 150 degrees