# The Space Geometry Savior

### A Dummy's Guide to the Basics of Space Geometry

## 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.