True Shapes of Sectioned Combinations

True Shapes of Sectioned Combinations

The Grade 10 true-shape method extends directly to combinations: project perpendicular to the cutting plane, transfer widths from the plan, and join in order. What changes is that the section now has several distinct parts, and each must be transferred separately.

The procedure:

1. Number the intersection points on each solid separately, as in the sectioning lesson.
2. Draw a new reference line parallel to the cutting plane.
3. Project every numbered point perpendicular to the cutting plane onto that line.
4. Transfer each point's width, measured from the centre line in the plan, onto its projector.
5. Join each solid's points in its own order.

Where widths come from. The plan holds the widths, because the plan is the view that shows the object's true width across the cut. Taking widths from the elevation is the classic error — the elevation shows heights, not widths.

Worked example. An inclined section through a cylinder on a prism gives a part-ellipse and a trapezium. Both are projected onto the same reference line, with each point's width transferred from the plan, so the two parts of the true shape end up correctly positioned relative to one another.

Core checkpoint: Projectors perpendicular to the cutting plane; widths from the plan. Those two rules produce the true shape every time.