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Hold a pencil at an angle under a desk lamp, and its shadow on the desk is noticeably shorter than the pencil itself.
In engineering graphics, an oblique line is a line tilted relative to all standard projection planes, so both its front and top views appear artificially foreshortened.
How can we find the actual length of that line and its exact tilt without guessing?

The Auxiliary View Principle

In 1795, French mathematician Gaspard Monge formalized descriptive geometry for military fortifications, proving that viewing a line from a perpendicular line of sight reveals its actual length.
To see the true length (TLTL) of an oblique line, you must position an auxiliary projection plane strictly parallel to that line's projection.
Now, where do the endpoints land on these new projection rays?

Step-by-Step True Length Construction

Start in the horizontal view (HH) and draw a reference fold line H/1H/1 parallel to segment ahbha_h b_h at any convenient distance.
Next, project lines from aha_h and bhb_h perpendicular to the fold line H/1H/1 into the new auxiliary view space.
To find where points a1a_1 and b1b_1 sit along those rays, apply the skip-one-view rule: transfer each point's perpendicular distance from the prior reference line.