Which lines establish the extent of a dimension and may not cross dimension lines?

The correct choice is the type of lines known as extension lines. These lines play a crucial role in technical drawings by indicating where a dimension begins and ends. They are drawn parallel to the dimension lines and extend from the object to the dimension line itself, clearly defining the limits of the measurement being provided.

Extension lines must not cross dimension lines, as that would create confusion in interpreting the dimensions being conveyed. Maintaining a clear separation ensures that anyone reading the drawing can quickly understand the specific measurements without misinterpretation.

In contrast, other lines mentioned in the options serve different purposes. Leader lines are used to connect a specific note or dimension to a point on a drawing, while dimension lines indicate the actual measurement values alongside an arrow to show the extent of the dimension—but do not establish where the measured points are. Construction lines are utilized for initial layouts and do not convey actual measurements or dimensions. This distinction further emphasizes the specific role that extension lines play in establishing measurement boundaries in engineering drawings.