3D Geometry Problems

Pro Tips

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.

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?".

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

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)