The Space Geometry Savior
A Dummy's Guide to the Basics of Space Geometry
The Basics to Orthogonality in Space
Property 1: Line Perpendicular to a plane
To prove (d) perpendicular to (P):
1. (d) perpendicular to (m) such that (m) c (P)
2. (d) perpendicular to (m') such that (m') c (P) such that (m) and (m') are intersecting.
NOTE: As soon as you prove that the line (d) is perpendicular to the plane (P) then automatically (d) is perpendicular to every line in (P).
Property 2: 2 Perpendicular Planes
To prove (Q) perpendicular to (P):
1. (d) perpendicular to (m) such that (m) c (P)
2. (d) perpendicular to (m') such that (m') c (P)
3. (d) c (Q)
NOTE: Proving that two planes are perpendicular is a DEAD END. You can't use it to prove something else later on.
Mediator Planes
A mediator plane is similar to the perpendicular bisector of a segment.
Property: Any point on a mediator plane is equidistant from the two extremeties of the segment.
Axis of a Circle
Given a circle (C):
1. of center I
2. line (d) perpendicular to (C) at I
So, (d) is the axis of a circle.
Property: Any point on (d) is equidistant from any point on (C).
NOTE: Proving any 2 will result in the third.
In the figure below, point G on (d) is equisdistant from the points A, B and C on the circle since (d) is the axis of the circle.