In a rhombus/parallelogram what's the relationship between the corner angles at the four vertices and the angles at the intersection of the diagaonal

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In a rhombus/parallelogram/trapezoid do the diagonals bisect the corner four angles at the vertices?

Is it possible to construct a non-rhombus by putting four 3-4-5 triangles where the right angle is not at the intersection of the two diagonals?

The following is a parallelogram

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Is there any relationship between the four angles formed at the intersection of the diagonals of a parallelogram and the four corner angles at the vertices of the figure?

Is this true or false, "The four angles formed at the intersection of the diagonals of a parallelogram are congruent." When is it true or false?