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True lengths in dihedral

A foreshortened projection is no good for measuring. To see a segment at real size there are two ways: change the projection plane until it is parallel, or spin it until it is parallel. Both get there; the change of plane is usually faster and the spin is easier to explain when there are many elements.

What you need to know

• Choose between change of plane and spin depending on the exercise.
• Change the horizontal or vertical plane without losing heights or distances.
• Spin a point around an axis perpendicular to a projection plane.
• See a plane edge-on and then in true shape.

How it is solved

1. Change of plane: choose the new ground line parallel or perpendicular to what you want to see.
2. Carry the heights (or distances) perpendicular to the new ground line, keeping the distance.
3. Spin: place the axis perpendicular to a projection plane and turn until the element is parallel.
4. Check that the size does not change: only the way it looks does.

How it appears in the exam

It appears as “true length of segment AB” and as the final step of distances and angles. With two changes of plane in a row an oblique plane is seen in true shape: first edge-on, then parallel.

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