SPACE SUMMARY

PROPERTIES AND RULES

Parallel Planes

If two planes are parallel and a plane cuts both, the two intersecting lines are parallel.

Also,

  • If two planes are parallel, then every line perpendicular to one is perpendicular to the other.
  • if two planes are perpendicular to the same line, then they are parallel.
  • If two lines are parallel, then every plane perpendicular to one is perpendicular to the other.
  • If two lines are perpendicular to the same plane, then they are parallel.

PERPENDICULAR PLANES

MEDIATOR PLANE

Definition: The plane through the midpoint of a line segment and perpendicular to that segment, also called a mediating plane.

Proof: Sets of points equidistant from two points

DIHEDRAL ANGLES

  • We call dihedral, the angle of the space limited between two semi-planes for frontier a common line.
  • Proof:
  1. Common line
  2. Select a straight line in the first plane perpendicular to the common line.
  3. Select a straight line in the second plane perpendicular to the common line.