The question doesn't state that the original toothpicks can't be used in the remaining three triangles (which most of the above solutions rely on also).
You can lay the three extra toothpicks on top of the original ones, making a triangle formed by the new toothpick and two original toothpicks
Original Two Three Four
/\ //\ /\\ /\
/ \ // \ / \\ / \
/____\ //____\ /____\\ /====\