Plane and Solid Geometry
Plane and Solid Geometry
This domain tests accurate geometric construction and spatial reasoning. You must construct plane figures and loci with compass and straightedge, then apply those skills to solids: orthographic views, true shapes, sections, developments and interpenetration.
Core rules
- Leave all construction arcs and lines visible; they are evidence of method.
- A perpendicular bisector is the locus of points equidistant from two points. An angle bisector is the locus equidistant from two lines.
- To construct a regular polygon, use its circumcircle: divide 360° by the number of sides to get the central angle, then step off equal chords.
- For solids, project every vertex. Hidden detail is dashed; centre lines locate axes of symmetry.
- A true shape is found by projecting perpendicular to a section plane or by an auxiliary view; an inclined face in a normal view is foreshortened, not true size.
Worked example
Construct a regular hexagon on a 40 mm side. Set compass radius to 40 mm and draw the circumcircle. The central angle is 360°/6 = 60°, and in a regular hexagon the side equals the radius, so the chord for each side is 40 mm. Mark point A on the circle, step the 40 mm chord around six times, and join consecutive points. Check that all six sides are equal and that opposite sides are parallel. The construction is exact because each triangle formed by two radii and a side is equilateral.
Traps
Using a ruler to construct instead of compass arcs; erasing construction lines; choosing the wrong side of a given line; confusing an auxiliary view with a true shape; and failing to project hidden edges consistently between views.