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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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Q: Why contour line never crosses another contour line?
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straight line


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