# Space Geometry

### Rules

## Parallel

**1-**

__How to prove (ABCD) // (EFGH) :__- (AB) // (EF) (AB) ∩ (BC)

- (BC) // (FG) (EF) ∩ (FG)

-(∆) ⊂ (P)

-(∆') ⊂(Q)

=>(d)//(∆) // (∆')

## Perpendicular

We prove (d)⊥ to 2 intersecting lines in (P)

## Example:

__Prove (AE) ⊥ (EFG)__**(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

**Example:**Prove: (AE) ⊥ (EG)

since (AE) ⊥ (EFG)

and (EG) ⊂ (EFG)

=> (AE) ⊥ (EG)

## Dihedral Angle

## 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

**Definition:**Mediator plane of [AB] is a plane ⊥ to [AB] at its midpoint

**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"