NO they can't
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For two dimensional lines: Get the formulas for the two lines into a format so that you can evaluate the slope. If the slopes are different, then they will intersect. If the slopes are the same, then you have two parallel lines, or possibly, the two equations describe the same line.
No, because although perpendicular and intersecting lines do touch, parallel lines never meet.
the definition of intersecting lines is: two lines that meet and cross at the same at the same place
No.
Two lines with the same slope are parallel.