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1.2 Points, Lines, and Planesthe 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

l

Read Line AB or Line l

- Infinite
- never ending, ongoing
- Finite
- limited number, terminates
- Collinear points
- points on the same line
- Noncollinear points
- points not on the same line

- Plane
- A flat surface without thickness that extends

infinitely in all directions

Name a plane with one capital letter that has no

point or with 3 noncollinear points

E

Plane F, Plane ABC, Plane BAC, Plane DAC or

Plane CBA , etc

D

- Coplanar points
- Points that lie in the same plane
- Noncoplanar points
- points that do not lie in the same plane

- Postulate or Axiom
- A statement that we assume is true or that we

accept as fact - Theorem
- A 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 1

Rectangular 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 points
- Noncoplanar points and space are the same

- Postulate
- 4 noncoplanar points determine space
- If 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).

- A,B,C
- E,F,C,B
- G,D
- E,F,A
- G,C,A,B
- F,C
- D,A,R

R

Give a reason for each answer!!!!

J

- Determine if the following are collinear,

coplanar, or noncoplanar. - E,D 5. A,C
- A,B,F 6. E,F,C,B
- G,C,B,A 7. B,D,E,H
- F,A,H,B 8. G,A

9. A, J, B

Postulate the intersection of 2 planes is a line

Plane SUY n Plane CSY in SY

Diagram 2

Explain the relationship between 2 planes.

They intersect in a line or they are parallel.

Diagram 3

Diagram 3

Give the intersection of the following

Plane UXV n Plane UXQ Plane UQR n Plane

XWS Plane VWS n Plane XUV

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

- A plane is determined by 2 intersecting lines.
- If 3 pts are coplanar, they are collinear.
- Any 2 pts are collinear.
- A plane and a line intersect at most in one pt.

- 3 points are not always coplanar.
- 2 planes intersect in infinitely many pts.
- 2 different planes intersect in a line.
- A line lies in one and only one plane.
- A line and a pt not on the line lie in one and

only one plane. - 3 planes can intersect in only one pt.

- 11. 3 lines can intersect in only one pt.
- 3 lines can intersect in only 2 points.
- The intersection of any 2 half-planes is

necessarily a half-plane. - 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