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Yes, it is possible for a shape to have at least one pair of parallel lines and no lines of symmetry. For example, an irregular trapezoid has one pair of parallel sides but lacks any lines of symmetry due to its uneven angles and side lengths. This demonstrates that parallel lines and symmetry are independent properties in geometric shapes.
No, they are not.
A quardrilateral with 1 pair of parallel lines and have no equal sides is a trapezium.
Yes, a pair of intersecting lines always forms a pair of vertical angles.
In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel. A simple example of a pair of skew lines is the pair of linesthrough opposite edges of a regular tetrahedron.