No, the diagonals of a parallelogram are not necessarily perpendicular.
A parallelogram is defined as a quadrilateral with opposite sides that are equal in length and parallel. One of the properties of parallelograms is that their diagonals bisect each other; this means that they cut each other in half. However, the angles between the two diagonals can vary depending on the specific shape of the parallelogram.
In a rectangle or a square, which are special cases of parallelograms, the diagonals are indeed perpendicular to each other. However, in most other types of parallelograms, such as rhomboids or general parallelograms, the diagonals will intersect at an angle that is not 90 degrees.
To summarize, while the diagonals of a parallelogram will always bisect each other, they are not always perpendicular. Only in specific types of parallelograms, like squares and rectangles, do they form right angles with each other.