Yes, any vertex is formed by two adjacent lines.
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square
Yes a square has 4 equal sides and 4 equal interior angles of 90 degrees
No. Consider a set of two or more parallel lines and pick any one of them. There will be another line adjacent to it. But, because it is parallel to the first, they cannot intersect.
The adjacent sides of a square are perpendicular.
A square by definition has lines of symmetry. Therefore a square cannot be drawn without any lines of symmetry.