Mesh.vertices and Mesh.uv Clarification

I am trying to make random shapes with a mesh, but my first step is to learn how to make a mesh programmatically. My question is simple. Why does A work, but B does not?

A (should be right triangle with right angle at top left and it works):

 void Start () {
     gameObject.AddComponent("MeshFilter");
     gameObject.AddComponent("MeshRenderer");
     Mesh mesh = GetComponent<MeshFilter>().mesh;
     mesh.Clear();
     mesh.vertices = new Vector3[] { new Vector3(0, 0, 0), new Vector3(0, 1, 0), new Vector3(1, 1, 0) };
     mesh.uv = new Vector2[] { new Vector2(0, 0), new Vector2(0, 1), new Vector2(1, 1) };
     mesh.triangles = new int[] { 0, 1, 2 };
 }

B (should be right triangle with right angle at bottom right...but nothing draws):

 void Start () {
     gameObject.AddComponent("MeshFilter");
     gameObject.AddComponent("MeshRenderer");
     Mesh mesh = GetComponent<MeshFilter>().mesh;
     mesh.Clear();
     mesh.vertices = new Vector3[] { new Vector3(0, 0, 0), new Vector3(1, 0, 0), new Vector3(1, 1, 0) };
     mesh.uv = new Vector2[] { new Vector2(0, 0), new Vector2(1, 0), new Vector2(1, 1) };
     mesh.triangles = new int[] { 0, 1, 2 };
 }