
Public learning track
Dihedral and Trihedral Multi-View Systems: Points and Lines
10th Grade · Math · Open Global Math
5 lessons
Goal
Represent points, line segments, and lines across horizontal, vertical, and profile projection planes using Monge's descriptive geometry.
Featured Diagrams
Principles of the Dihedral System and the Monge Epure
5 lessons
0 of 5 done
- 1Principles of the Dihedral System and the Monge EpureUp nextStart
- 2Projecting Points in Dihedral and Trihedral SpacesPremiumNot started yet
- 3Classifying Lines and Their Traces in Multi-View SystemsNot started yet
- 4Finding the True Length and Inclination of a Line SegmentNot started yet
- 5Relative Positions of Lines: Parallel, Intersecting, and SkewNot started yet
Standards Covered
- 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.
- 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.
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.