1.2 points, lines, and planes the 3 undefined terms of geometry geometry
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Point No size, no dimensions, it only has position
A true point cannot be seen with the naked eye
Name a point with a capital letter.
A Note the dot is only a representation of a pt.
Line
An infinite number of points that extends in 2 directions
Name a line with 2 points(2 capital letters)
Or with one lower case letter
A B lRead Line AB or Line l
Infinite never ending, ongoing
Finitelimited number, terminates
Collinear points points on the same line
Noncollinear points points not on the same line
PlaneA flat surface without thickness that extends infinitely in all directions
FA
BC
Name a plane with one capital letter that has no point or with 3
noncollinear pointsPlane F, Plane ABC, Plane BAC, Plane DAC
or Plane CBA , etc
D
E
Coplanar points
Points that lie in the same plane
Noncoplanar points
points that do not lie in the same plane
Postulate or AxiomA statement that we assume is true
or that we accept as factTheoremA statement that must be proven
true.You use definitions, postulates and
other theorems to prove theorems true.
Basic Postulates
2 points determine a line.
2 lines intersect in a point
2 planes intersect in a line
3 planes intersect in a point or a line
If 2 pts lie in a plane, then the plane
contains every pt on the line.
Parallel lines
Coplanar lines that never intersect
Skew lines
Noncoplanar lines that never intersect
4 postulates4 ways to determine a plane
• 3 noncollinear pts determine a plane
• A line and a pt not on the line determine a plane
• 2 ll lines determine a plane
• 2 intersecting lines determine a plane
Postulate4 noncoplanar points
determine spaceIf you can make skew lines out of 4 pts, then you know you are in
space.
Postulates
An infinite number of planes can be passed through a line.
Or a line determines an infinite number of planes.
Any 2 points are collinear
Any three points lie in the same plane
Only 3 noncollinear points determine one plane
Skew lines always indicate space
Determine if the following sets of points are collinear, noncollinear (coplanar), or noncoplanar
(space).1.A,B,C
2.E,F,C,B
3.G,D
4.E,F,A
5.G,C,A,B
6.F,C
7.D,A,R
Give a reason for each answer!!!!
R
Determine if the following are collinear, coplanar, or noncoplanar.
1. E,D 5. A,C
2. A,B,F 6. E,F,C,B
3. G,C,B,A 7. B,D,E,H
4. F,A,H,B 8. G,A
J
9. A, J, B
Give the intersection of the following:
Plane UXV ∩ Plane UXQ
Plane UQR ∩ Plane XWS
Plane VWS ∩ Plane XUV
Diagram 3
• Distribute Geometry Plane and Simple worksheet # 5
• Allow students to work together for about 5 to 10 minutes
Hapless HairlineTrue/False
1. A plane is determined by 2 intersecting lines.
2. If 3 pts are coplanar, they are collinear.
3. Any 2 pts are collinear.
4. A plane and a line intersect at most in one pt.
5. 3 points are not always coplanar.
6. 2 planes intersect in infinitely many pts.
7. 2 different planes intersect in a line.
8. A line lies in one and only one plane.
9. A line and a pt not on the line lie in one and only one plane.
10. 3 planes can intersect in only one pt.
11. 3 lines can intersect in only one pt.
12. 3 lines can intersect in only 2 points.
13.The intersection of any 2 half-planes is necessarily a half-plane.
14.The edge of a half-plane is another half-plane.