Space Geometry
Rules
Parallel
- (AB) // (EF) (AB) ∩ (BC)
- (BC) // (FG) (EF) ∩ (FG)
-(∆) ⊂ (P)
-(∆') ⊂(Q)
=>(d)//(∆) // (∆')
Perpendicular
We prove (d)⊥ to 2 intersecting lines in (P)
Example:
(AE) ⊥ (EF) (AEFB is a rectangle)
(AE) ⊥ (EH) (AEHD is a rectangle)
=> (AE) ⊥ (EFH) = (EFG)
2- If a line is perpendicular to a plane then it is perpendicular to any line contained in this plane
Prove: (AE) ⊥ (EG)
since (AE) ⊥ (EFG)
and (EG) ⊂ (EFG)
=> (AE) ⊥ (EG)
Dihedral Angle
Angle between two planes
2) Select straight line in (P) ⊥ (AB)
3) Select a straight line in (Q) ⊥ (AB)
4) Find the angle using any method in geometry (trigonometry, triangles, circles..)
Angle between line and a plane
1- Make the orthogonal projection from (d) to (P)
2- Find the angle using any method in geometry (trigonometry, triangles, circles..)
Mediator plane
Property: Any point on Mediator Plane is equidistant from the extremities.
You can prove a mediator plane by proving 3 points on Mediator Plane equidistant from extremities
Perpendicular planes
prove a plane (P) perpendicular to a line (d) contained in (Q)
=> (P) ⊥ (Q)
Parallel Planes
Prove two intersecting straight lines parallel in (P) parallel to two intersecting straight lines in (Q)
Axis of Circle
Done By:
Grade 11 "B"