1.2 Points, Lines, and Planes

the 3 undefined terms of Geometry

Geometry

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.

Diagram 1Rectangular Prism – faces are rectangles and bases are always parallel

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

Space

The set of all pointsNoncoplanar points and space are the same

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

Postulate – the intersection of 2 planes is a line

Plane SUY ∩ Plane CSY

in SY

Diagram 2

Explain the relationship

between 2 planes.

They intersect in a line or they are parallel.

Diagram 3

Give the intersection of the following:

Plane UXV ∩ Plane UXQ

Plane UQR ∩ Plane XWS

Plane VWS ∩ Plane XUV

Diagram 3

Explain the relationship

between a line and a plane.

They intersect in a pt or a line.

Diagram 4

• 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.

assign pgs. 13-15 ( 1-51 odd), (60-66 all) hw

Diagram 1

Diagram 2

Diagram 3

Diagram 4