point, line, and plane postulates
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Point, Line, and Plane Postulates. Section 2.4. 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 ruler Postulate 2 = Segment Addition Postulate - PowerPoint PPT PresentationTRANSCRIPT
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