SPACE

3D - The real dimensions

Objectives

- Line parallel to a plane

- Parallel planes

- Line perpendicular to a plane

- Perpendicular planes

- Determination of angle between 2 planes

- Mediator plane

- Axis of a circle

- Bisector plane


Line Parallel to A Plane

A line and a plane are parallel if they do not intersect.


How to prove?

Prove the line is parallel to a line in the plane.

Parallel Planes

Two planes are parallel if 2 intersecting lines of the first plane and parallel to 2 intersecting lines of the other.


Line Perpendicular to a Plane

A line is perpendicular to a plane if it's perpendicular to 2 intersecting lines in the plane.

Determination of angle between 2 intersecting planes

1. Determine the common line

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

3. Select a straight line in second plane perpendicular to common line.


The angle in that between the first determined straight line and the second.

Mediator Plane

What's a mediator plane?

A mediator plane is a plane perpendicular to a segment at its midpoint.

Any point on the mediator plane is equidistant to the extremities of the segment.


How to prove it?

M1: Prove 3 points on the plane equidistant to the extremities of the segment.

M2: 1) D*[AB]

2) DA=DB, OA=OB, CA=CB

3) (DOC) mediator plane


Bisector Plane

It's a plane that bisects a dihedral angle formed by 2 planes into 2 equal angles.