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
1.
A line l is perpendicular to plane A if l is perpendicular to all of the lines in plane A that intersect l. A plane B is perpendicular to a plane A if plane B contains a line that is perpendicular to plane A.
2.
If two planes are perpendicular to the same plane, then the two planes either intersect or are parallel: plane B ⊥ plane A, plane C ⊥ plane A, and plane B and plane C intersect along line l.
3.
Two intersecting planes that are perpendicular to the same plane: plane B ⊥ plane A, plane C ⊥ plane A, and plane B // plane C.
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:
- Common line
- Select a straight line in the first plane perpendicular to the common line.
- Select a straight line in the second plane perpendicular to the common line.