How can I tell whether two line segments are equal in length from a diagram?

Not from appearance alone. A drawing can make unequal segments look equal, or equal segments look slightly different because of how it was drawn or displayed. First look for information that tells you what the diagram means: matching marks on the segments, a written equality statement, or another given fact that establishes their lengths.

For sides in the triangle diagrams covered by OpenStax, the same number of hash marks on two sides denotes equal lengths [S1]. That is a notation clue, not a reason to assume every similar-looking pair is equal. If the problem provides no relevant marks or statement, describe the segments as appearing similar rather than conclude they are equal.

Compare the marks drawn across the segments, not the apparent lengths of the lines. In the triangle diagrams addressed by the cited source, sides with the same hash-mark pattern have equal lengths [S1]. For example, if two triangle sides each have one short tick and the third has two, the one-tick sides are marked as equal to each other. The marks assert equality even if the drawing does not look perfectly precise.

Check that the marks really are on the segments you are comparing and have the same pattern. Do not treat ordinary grid lines, corners, shading, or other diagram details as equality marks unless the problem explains them that way. The cited convention concerns triangle diagrams; it does not establish what every other kind of diagram notation means.

You can measure both segments with the same ruler as a practical check. Put the ruler’s zero at one endpoint of the first segment, note the other endpoint, then repeat for the second using the same units. Keep the ruler aligned with each segment. Write down the readings instead of relying on a visual comparison.

For example, suppose your measurement notes say AB is about 4.2 cm and CD is about 4.2 cm. You can report that they measure the same to the nearest millimetre on your ruler. That is an estimate from the drawing, not proof that the original mathematical lengths are exactly equal. A small drawing, thick lines, or limited ruler precision can make close lengths hard to distinguish. Check whether the exercise expects you to use stated geometry information rather than measurements from the picture.

Say what your evidence is, and distinguish a diagram mark from a physical measurement. For a marked triangle, you could write: “The two sides have matching tick marks, so the diagram indicates that their lengths are equal.” This follows the hash-mark convention described for the triangle diagrams in the source [S1].

If you measured instead, make the limitation clear: “On this printed diagram, both segments measure about 4.2 cm with the same ruler, so they appear equal to that measurement precision. The picture alone does not establish exact equality.” If neither marks nor measurements nor a written relationship are available, say that the diagram does not provide enough information to determine equality. The source confirms a notation convention for its triangle diagrams; it does not establish that a particular unmarked pair is equal or define conventions for every diagram.