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No. Most parallelograms do not have perpendicular angles.

When a parallelogram has perpendicular angles, it's classified as a Rhombus. Rhombi are special parallelograms in that all four sides are of equal length, and it is because these sides are all of equal length that the rhombus achieves diagonal perpendicularity.

(See diagram in the "sources and related links" below)

Should one set of parallel lines be longer or shorter than the other set, the parallelogram skews, or "Squishes," which "bends" the interior angles of the intersect of the diagonals--that is, one set of vertically opposite angles becomes acute, the other, obtuse.

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Q: Do all parallelograms have perpendicular diagonals?
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