Public learning track
Spatial Rotations, Rabatment, and Solid Sections
10th Grade · Math · Open Global Math
6 lessons
Goal
Apply spatial rotation and rabatment methods to find true metric properties, plane intersections, and planar sections of complex geometric solids.
Featured Diagrams
Spatial Rotation of Points and Lines Around Projecting Axes
6 lessons
0 of 6 done
- 1Spatial Rotation of Points and Lines Around Projecting AxesUp nextStart
- 2Spatial Rotation of Planes into Principal PositionsPremiumNot started yet
- 3Rabatment of Planes onto Reference Projection PlanesNot started yet
- 4Planar Sections and True Shapes of Cut PolyhedraNot started yet
- 5Planar Cuts and Conic Sections of Cylinders and ConesNot started yet
- 6Interpenetration and Intersection Curves of Solid BodiesNot started yet
Standards Covered
- OGM.11.DES.2Open Global Math Standards 2026™ · Math · Level 11 / High School 2 (Age 15) · Grade 10Determine intersections, parallelism, and perpendicularity between lines and planes in multi-view projection systems; apply auxiliary projection methods including changes of dihedral projection planes and 3D spatial rotations to analyze complex geometric solids.
- OGM.11.DES.1Open Global Math Standards 2026™ · Math · Level 11 / High School 2 (Age 15) · Grade 10Apply principles of descriptive geometry and spatial projection systems (dihedral, trihedral, orthographic, axonometric, cylindrical, and spherical systems) to represent points, lines, segments, planes, planar figures, and 3D solids.
Curriculum Framework
10th Grade · Math · Open Global Math
1
5 lessons
Dihedral and Trihedral Multi-View Systems: Points and Lines
Represent points, line segments, and lines across horizontal, vertical, and profile projection planes using Monge's descriptive geometry.
2
4 lessons
Planes and Planar Figures in Multi-View Systems
Construct and analyze general and special-position planes, planar traces, and 2D figures embedded in 3D projection spaces.
3
5 lessons
Axonometric, Cylindrical, and Spherical Projection Systems
Construct pictorial and curved-surface spatial representations using isometric, dimetric, trimetric, cylindrical, and spherical projections.
4
5 lessons
Spatial Intersections, Parallelism, and Perpendicularity
Solve spatial relationship problems involving intersections, parallelism, and perpendicularity between lines and planes in multi-view projections.
5
7 lessons
Auxiliary Projections and Change of Dihedral Planes
Transform general lines and planes into special positions using successive auxiliary reference planes to solve metric and spatial problems.
6
6 lessons
Spatial Rotations, Rabatment, and Solid Sections
Apply spatial rotation and rabatment methods to find true metric properties, plane intersections, and planar sections of complex geometric solids.