3D Geometry Problems
Pro Tips
Pro Tips
The way to approach 3D Geometry Problems is to tackle them as a composition of plane figures.
The way to approach 3D Geometry Problems is to tackle them as a composition of plane figures.
Redraw the triangles if you have difficulty visualising them on a flat plane.
Redraw the triangles if you have difficulty visualising them on a flat plane.
Try to look for triangles which are helpful (Eg. Right-Angled Triangles, Isosceles Triangles, Triangles which you know the value of multiple sides and/or angles). Then apply either TOA, CAH, SOH, Pythagoras' Theorem, Sine Rule or Cosine Rule to find the unknown lengths/angles.
Try to look for triangles which are helpful (Eg. Right-Angled Triangles, Isosceles Triangles, Triangles which you know the value of multiple sides and/or angles). Then apply either TOA, CAH, SOH, Pythagoras' Theorem, Sine Rule or Cosine Rule to find the unknown lengths/angles.
Work your way to the value you want. Ask yourself: "What length or angle would be helpful to me? Can I find that first? What else could be helpful? Is there any unknown length or angle that I can find right now?".
Work your way to the value you want. Ask yourself: "What length or angle would be helpful to me? Can I find that first? What else could be helpful? Is there any unknown length or angle that I can find right now?".
Think of 3D Geometry problems like solving a Sudoku, to find C, you might need B and to find B, you might need A.
Think of 3D Geometry problems like solving a Sudoku, to find C, you might need B and to find B, you might need A.
Diagonals
Diagonals
In a polyhedron, a diagonal is defined as a line segment connecting two vertices that are not along the same edge. There are 2 types of diagonals: (1) A face diagonal connects two vertices on the same face (aka exterior of the polyhedron) and (2) A space diagonal that connects two vertices on seperate faces of the polyhedron (aka interior of the polyhedron)
In a polyhedron, a diagonal is defined as a line segment connecting two vertices that are not along the same edge. There are 2 types of diagonals: (1) A face diagonal connects two vertices on the same face (aka exterior of the polyhedron) and (2) A space diagonal that connects two vertices on seperate faces of the polyhedron (aka interior of the polyhedron)
Explore!
Explore!
Use the applet below to explore how the length of a face diagonal and a space diagonal of a cuboid can be computed using Pythagoras' Theorem.
Use the applet below to explore how the length of a face diagonal and a space diagonal of a cuboid can be computed using Pythagoras' Theorem.
Right Rectangular Pyramid
Right Rectangular Pyramid
A rectangular pyramid has a rectangular base. In a right rectangular pyramid, the apex (highest point) likes directly above the midpoint of the base diagonal. All the lateral faces of this pyramid are isosceles triangles.
A rectangular pyramid has a rectangular base. In a right rectangular pyramid, the apex (highest point) likes directly above the midpoint of the base diagonal. All the lateral faces of this pyramid are isosceles triangles.