Because the lines between each vertice of the figure are already drawn.
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No, the diagonals of a parallelogram do not necessarily bisect the angles. The diagonals of a parallelogram divide it into four congruent triangles, but they do not necessarily bisect the angles of those triangles.
No, for the simple reason that triangles do not have diagonals.
Yes
Two triangles can be formed by the diagonals of one vertex of a four-sided polygon.
If you mean an isosceles triangle then no because all triangles have no diagonals