Fundamentals of contouring: choose the correct set of properties Select the option that correctly states key properties of contour lines on topographic maps.

Introduction / Context:
Contours are the backbone of representing three-dimensional terrain on a two-dimensional map. Understanding their geometric and topological properties helps interpret slopes, ridges, valleys, and depressions accurately. This item reviews three fundamental properties every surveyor must know.

Given Data / Assumptions:

• Contours represent loci of equal elevation.
• Standard mapping conventions apply (no overhangs shown in a single-valued surface representation).
• Continuous, differentiable ground surface assumed for interpretation.

Concept / Approach:

(a) On a single-valued surface representation, contours of the same elevation do not cross; two distinct same-elevation contours will not merge to form a longer line unless they are in fact the same contour closing elsewhere. (b) A contour is a closed curve; if it appears to end, it continues off the sheet. (c) The gradient vector is normal to the contour; hence, steepest slope is at right angles to the contour line at a point.

Step-by-Step Solution:

Verification / Alternative check:

These properties are consistent with level curves in calculus and standard cartographic rules.

Why Other Options Are Wrong:

Any subset of the properties omits essential facts; hence (d) is the most complete and correct choice.

Common Pitfalls:

Assuming contours can terminate; misinterpreting steepness by spacing along, rather than perpendicular to, contours.

Final Answer:

All of the above