No, a quadrilateral cannot be both. If two sides cross and self-intersect, their four endpoints must lie within the same unique plane determined by those intersecting lines, making the entire figure strictly planar.
Ganita Manjari part 2 Chapter 12.1 Solutions
Class 9 Ganita Manjari Part 2 Chapter 12 Page 56 Question Answer
No, it is impossible for a quadrilateral to be both self-intersecting and non-planar. By definition, a self-intersecting quadrilateral has two non-adjacent edges that cross at a shared intersection point. Two intersecting straight lines uniquely define a single flat plane containing both segments. Consequently, all four vertices must lie on that identical geometric plane, which forces the figure to remain planar rather than non-planar.
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