Space

The Summary

A plane is determined by

  1. 3 non-collinear points
  2. A line and a point outside the plane
  3. 2 intersecting lines
  4. 2 parallel lines

How to prove a line perpendicular to a plane ?

If a straight line is perpendicular to 2 intersecting lines in a plane then its perpendicular to the plane itself.
When Is a Line Perpendicular to a Plane? : Trigonometry & Other Math

And this means that if a line is perpendicular to a plane, then its perpendicular to every line in the plane!

Relative position of a plane and a line :

  1. Intersecting
  2. Parallel
  3. The line is in the plane

Relative position of 2 lines :

  1. Skew
  2. Parallel
  3. Intersecting
  4. Confounded

How to prove that 2 planes are perpendicular ?

Relative position of 2 planes :

  1. Intersecting
  2. Parallel
  3. Confounded

Angle between 2 planes - Dihedral angle

The Steps :

1- Find the common line.

2- Select 2 lines perpendicular from each plane to the common line.

3- Find the angle.

Mediator Plane

Property : Any point on the mediator plane of a line is equidistant from the extremities of this line.

How to prove a mediator plane to a line ?

Prove that it has 3 points equidistant from the extremities of the line.

The Angular bisector

Property : Any point on the angular bisector of an angle is equidistant from the sides of the lines forming this angle.

How to prove 3 collinear points?

Prove that they belong to a line that is the intersection of 2 planes

The End