Polygon Tessellation Problem

My polygon is a triangle with 3 summits and 2 points on one of the triangle side:
Idx:X,Y,Z
0:0,20,0
1:10,0,0
2:10,10,0
3:10,30,0
4:10,40,0

The tessellation return :
triangle1:014
triangle2:421
triangle3:423

those are not valid triangles since they use points that are on the same line.

Id’like to have :
triangle1:043
triangle2:032
triangle3:021

What can I do?