# Space

### Summary

## Parallel Planes and Lines

*(P) is parallel to (Q)

and

(Q) is parallel to (R)

then

(P) is parallel to (R)

*(P) is parallel to (Q)

and

the intersection of (P) and (R) is (d)

then

the intersection of (R) and (Q) is (d') which is parallel to (d)

## How to prove that a straight line is parallel to a plane?

(d) parallel to (d') + (l) parallel to (l') + (d) and (l), and (d') and (l') intersect.

## Two planes intersect at a straight line

## Perpendicular Planes and Lines

## How to prove that a straight line is perpendicular to a plane?

(d) perpendicular to (P)

then

(d) is perpendicular to any line in (P)

(P) is parallel to (Q)

and

(Q) is perpendicular to (R)

then

(P) is perpendicular to (R)

## How to prove two Planes perpendicular?

## Shapes

## angle between a line and a plane

## How to find?

2) Find angle between these 2 lines.

## Dihedral Angle

## How to find?

1) Find the common straight line.

example: (BC)

2) Select a straight line in the first plane perpendicular to the fist to the common line.

example: (SB)

3) Similarly select one in the second plane.

example: (AB)

The angle is SBA

## Mediator Plane

## Property

## How to prove?

a) Prove 3 non-cillinear points on the plane equidistant from the extremities.

b) By the property

## Angular Bisector

## How to prove?

a) Prove that the angle between (P) and (R) = the angle between (Q) and (R).

b) Prove any point on (R) equidistant from (P), (Q), and the line of intersection.

## Axis of a circle

## Definition

## Property

## How to prove?

a) AB=AC=AD

and

(AO) is perpendicular to (C)

b) By definition

## Done by:

Ghida Ladkani

Marlene Al Abed