point, line, and plane postulates

SECTION 2 .4

Point, Line, and Plane Postulates

Note-Taking Guide

I suggest only writing down things in red

Review of Postulates from Chapter 1

Postulate 1 = Rule Postulate Basically you can measure length/distance with a

rulerPostulate 2 = Segment Addition Postulate

If is between and then Postulate 3 = Protractor Postulate

Basically you can measure angles with a protractorPostulate 4 = Angle Addition Postulate

If is in the interior of then

New Postulates in Section 2.4

More statements about points, lines, and planes we accept without having to prove them

The reason we are learning these is to eventually use them to prove other things

Plane, Line, and Point Postulates

Postulate 5Through any two

points there exists exactly one line

Plane, Line, and Point Postulates

Postulate 6A line contains at

least two points

Plane, Line, and Point Postulates

Postulate 7If two lines intersect,

then their intersection is exactly one point

Plane, Line, and Point Postulates

Postulate 8Through any three

noncollinear points there exists exactly one plane

Plane, Line, and Point Postulates

Postulate 9A plane contains at

least three noncollinear points

Plane, Line, and Point Postulates

Postulate 10If two points lie in a

plane, then the line containing them lies in the plane

Plane, Line, and Point Postulates

Postulate 11If two planes

intersect, then their intersection is a line

Definition

Definition of Perpendicular Figures:

A line is to a plane if and only if the line is to every line in the plane that it intersects

Notice how line is to line and line and any other line we could draw in plane

Interpreting Diagrams

What stuff are we allowed to assume in this diagram? Coplanar points Points on drawn in

lines are collinear

Interpreting Diagrams

What stuff are we NOT allowed to assume in this diagram? Points without drawn in

lines are collinear Ex: G, F, E

Coplanar lines intersect Coplanar lines do not

intersect Ex: we do not know if and

intersect, but we do not know that they don’t intersect

Congruency Perpendicular

Boardwork

Find a marker and a spot at the board

True or False

Two planes intersect in exactly one point.False

True or False

A plane contains at least 3 noncollinear points.

True

True or False

Through any two points there exists exactly one line.

True

True or False

If two points are on a plane, then the line containing those points is off of the plane.

False

True or False

If two lines intersect, then their intersection is exactly two points.

False

True or False

A line is made up of exactly two points.False

Practice Problems T or F: is in plane

True State the intersection of plane

and plane

T or F: and intersect True

T or F: and intersect False

T or F: and intersect False (there is not enough

information to assume one way or the other, so since there the potential for the statement to be false, the statement is not true 100% of the time and thus the correct answer is False)

Practice Problems

T or F: plane exists True

T or F: are coplanar False (it could potentially

be false, so answer cannot be true 100% of the time, so correct answer is False)

T or F: is to plane False (it could potentially

be false, so answer cannot be true 100% of the time, so correct answer is False)

Practice Problems

Name a line to plane

T or F: is in plane True (even though the line

is not drawn in, we know that since the points are in the plane that the line must be in it as well)

T or F: True (even though the line

is not drawn in, since we know is to plane it must be to every line drawn in the plane

Practice Problems

T or F: plane plane True Definition of

perpendicular planes: Planes that intersect

so that intersecting lines, one in each plane, form a right angle