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Q: What shape has 2 pairs of parallel sides equal length of diagonals which do not cross at 90 degrees?

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No.

The cross section of cylinder along its length (parallel to the axis of symmetry has the shape of a rectangle.

The diagonals of a rectangle do not cross at right angles

The diagonals of a square and a rhombus cross at right angles.

It depends on the inclination of the line of cross section. If it is at an incline to the sides and diagonal, the cross section is a point which becomes a line that increases in length, reaches a maximum, remains at that length and then shrinks back to a point. If it is parallel to a diagonal, the cross section is a point which becomes a line that increases in length, reaches a maximum and then shrinks back to a point. If it is parallel to a side, the cross section is a line of constant length.

Related questions

A rectangle

A parallelogram (or rectangle) which is not a rhombus (or square).

A rectangle would fit the given description

A rectangle.

No.

The diagonals do not intersect (cross) at 90 degrees.

Because it has 4 sides of equal lengths and its diagonals cross at 90 degrees. It looks like a tilted square with opposite parallel sides

yes, they do. though they are not always equal in length they always cross at right angles.

A parallelogram

The cross section of cylinder along its length (parallel to the axis of symmetry has the shape of a rectangle.

The diagonals of a rectangle do not cross at right angles

The diagonals of a square and a rhombus cross at right angles.

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