The Space Geometry Savior

A Dummy's Guide to the Basics of Space Geometry

The Basics to Orthogonality in Space

So you're probably checking out this flyer right now because it's your last attempt to understand space geometry! It's pretty simple as long as you keep up with the properties and the conditions for their applications. Here goes nothing.

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.

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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.

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GOOD LUCK!

Well, this is as far as I go! Feel free to visit these links below for extra information on angles in space and other properties.