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Distances in the dihedral system
Measuring a distance in dihedral always follows the same scheme: find the perpendicular, find the foot and measure the segment in true length. What changes is what the perpendicular is drawn to and how the segment is then rotated flat to see it at real size.
What you need to know
- Point to plane: perpendicular through the point, foot and true length.
- Point to line: plane perpendicular to the line through the point.
- Between two skew lines: a plane parallel to one that contains the other.
- Between parallel planes: measured along a common perpendicular.
How it is solved
- Draw the perpendicular to the reference element (line or plane) through the point.
- Find where that perpendicular meets the element: that is the foot.
- Rotate the point-foot segment flat or bring it to true length with a change of plane.
- Measure on the true length, never on a projection.
How it appears in the exam
“Find the distance from point P to plane α” is a classic. It also appears as point to line and, less often, between skew lines. The typical mistake is measuring the segment as it is in the elevation or the plan: there it is not in true length.
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