Each contour line represents a different elevation. If they touched at any point, that would mean that point would have 2 different elevations at once, which doesn't make any sense. They can get really close if there is a steep drop, but they never touch.
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They can never cross but they converge as the represented ground steepens, so they touch in appearance on paper when representing a vertical face of height at least equal to the difference between two consecutive lines.
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A line intersect is a point on a line where another line or object crosses the line.
Perpendicular lines are where a line crosses another line and forms 4 right angles on all 4 sides but a intersecting line only crosses another line
because the world would explode
lower.