Add triangle to empty mesh

I like to simply add, for example a new triangle to an existing or empty mesh. Like:

mesh = open3d.geometry.TriangleMesh()
t1 = numpy.asarray([[2,2],[5,2],[5,5]])

which would than create the edges in counter-clockwise way (for determining the normal direction). I can however not find any such functionality beside methods like ‘create_torus’ to actually generate geometry other than loading it from file.
How is the approach in Open3D when creating geometry from scratch with defined polygons and also how to add single points/vertices to a open3d.geometry.PointCloud. I searched for every standardized keywords like add, append, insert, push_back but it looks like the classes are missing the most basic functionality.

Thanks in advance