Does adding a point to a triangle make it a quadrilateral? and if so can a triangle be any polygon?

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Does adding a point to a triangle make it a quadrilateral? and if so can a triangle be any polygon?

does the next triangle a quadrilateral?

Image of 4 points on a triangle. Is this a quadrilateral?

Or, does a point have to change a side angle?

Thank you for any help, I am new here and I opened this question because of an argument with my math teacher and classmates.