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Solid two planes

Two planes parallel to each other

If there is no common point between two planes, then these two planes parallel.

Two planes parallel to each other
S is a plane. T is another plane. Since there is no common point between planes S and T, then the plane S parallel to plane T.

The position relation of two planes

1. When two plane parallel, there is no common point.
2. When two plane intersect, there is one common line.
The position relation of two planes.
In the figure above, when plane T intersects the plane S, there is one line c generated.

Determine whether two plane parallel theorem 1

If two intersected lines in a plane parallel to another plane, then these two planes parallel.

Determine whether two plane parallel theorem
In the figure above, c and d are two intersected lines on the plane S. If line c parallel to plane T and line d also parallel to plane T, then the plane S parallel to plane T.

Determine whether two plane parallel theorem 2

Two planes that perpendicular to the same line parallel.

.Determine whether two plane parallel theorem 2
In the figure above, S is a plane, T is another plane and e is a line. If line e perpendicular to plane S and line e also perpendicular to plane T, then plane S parallel to plane T.

Property of two planes parallel theorem 1

If two lines parallel, then a line on a plane parallel to another plane.

what is the property of two parallel planes?
In the figure above, c is a line on the plane S. If plane S parallel to plane T, then line c parallel to plane T.

Property of two planes parallel theorem 2

If two parallel planes intersect the third plane, then their intersected lines parallel.

what is the property of two parallel planes?
In the figure above, e is the intersected line when plane R intersects plane S. f is the intersected line when the plane R intersects the plane T. If plane S parallel to plane T, then line e parallel to line f.

Property of two planes parallel theorem 3

If a line perpendicular to one of two parallel planes, then the line also perpendicular to another plane.

what is the property of two parallel planes?
In the figure above, plane S parallel to plane T. If line c perpendicular to plane S, then line c also perpendicular to plane T.
Since line c perpendicular to both plane S and plane T, so line c is called the common perpendicular line of plane S and plane T.

Distance between two parallel planes

The figure below, plane S parallel to plane T, line c perpendicular to planes S and T. The perpendicular line c intersects the plane S and plane T at point A and B respectively, then the line segment AB is the distance between two parallel planes S and T.

what is the property of two parallel planes?

Two plane angle

A line in a plane divide the plane into two parts, each part is called half plane. The figure that made from the common edge and two half plane is called the two plane angle. This line is called the edge of the two plane angle. Each half plane is called the plane of the two plane angle.

the figure show what is the two plane angle.
The two plane angle is written as plane - edge - plane, that is, T - EF - S, or T - l - S.

Make the plane angle of the two plane angle (Definition method)

In the figure below, O is any point on the edge l. Draw a line that pass point O and perpendicular to edge l in the plane S, which is line segment OA. Draw another line that pass the point O and perpendicular to the edge l in the plane T, which is the line segment OB. The angle AOB is the plane angle of the two plane angle S - l - T.

The definition method of the plane angle of the two plane angle.

Make the plane angle of the two plane angle (Make a plane perpendicular to the edge method)

In the figure below, O is any point on the edge l. Draw a plane Q that pass the point O and perpendicular to the edge l. The plane Q intersects the plane S at the line segment OA. The plane Q intersects the plane T at the line segment OB. The angle AOB is called the plane angle of the two plane angle S - l - T.

The perpendicular plane method of the plane angle of the two plane angle.

Make the plane angle of the two plane angle (Three perpendicular lines method)

In the figure below, make any point A on the S plane of the two plane angle S - l - T, draw a line pass the point A and perpendicular to the edge l, which is the line segment AO. Draw another line that pass the point A and perpendicular to the plane T at point B, (B is the perpendicular point), connect BO, then the angle AOB is the plane angle of the two plane angle S - l - T.

The three perpendicular lines method of the plane angle of the two plane angle.

When the plane angle of the two plane angle S - l - T is 90o, the plane S perpendicular to plane T. The range of the plane angle of the two plane angle is: 0o <= angle AOB <= 180o.