2. Chapter 1-2 Points, Lines, and Planes

3. Objective Points, Lines, & Planes
To understand basic terms and postulates of geometry.

4. What is a definition? Known words used to describe a new word
Undefined terms – not formally defined
There are 3 in geometry.
Point Line Plane
Segments, rays, and angles are defined in terms of these basic figures.

5. Example what your Cornell notes should look like now
Points, Lines, & Planes Heading
Objectives: Date:
What is a definition Undefined terms……..

6. Point 1. Has no dimension (no length, width, thickness)
2. Usually represented by a dot
3. Named using one capital letter B

7. Points Points do not have actual size. How to Sketch: Using dots
How to label:
Use capital letters
Never name two points with the same letter
(in the same sketch). A B C A

8. Line Extends forever in one dimension (length)
Has an arrowhead on each end representing the fact that it goes on forever
Consists of an infinite amount of points
Always straight l A B

9. Lesson 1-1 Point, Line, Plane
Lines
Lines extend indefinitely and have no thickness or width.
How to sketch : using arrows at both ends.
How to name: 2 ways
(1) small script letter – line n
(2) any two points on the line -
Never name a line using three points - n A B C
Lesson 1-1 Point, Line, Plane

10. Plane Extends forever in 2 dimensions (length & width)
A flat surface consisting of infinitely many points
Usually represented by a 4-sided figure
NOT THIS!
THIS A W C B

11. Planes How to sketch: Use a parallelogram (four sided figure)
How to name: 2 ways
(1) Capital script letter – Plane M
(2) Any 3 non collinear points in the plane -
Plane: ABC/ ACB / BAC / BCA / CAB / CBA A M B C
Horizontal Plane
Vertical Plane
Other

12. Different planes in a figure:B
Plane ABCD
Plane EFGH
Plane BCGF
Plane ADHE
Plane ABFE
Plane CDHG
Etc. D C E F H G

13. More Definitions Collinear points – points that lie on the same line
Coplanar points –
points that lie on the same plane

14. Practice : Naming Points
Name a point that is collinear with the given points
B and E:
C and H:
D and G:
A and C:
H and E:
G and B:

15. Name a point that is coplanar with the given points
M, N, R:
M, N, O:
M, T, Q:
Q, T, R:
T, R, S:
Q, S, O:

16. Lesson 1-1 Point, Line, Plane
Coplanar Objects
Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible.
Are the following points coplanar?
A, B, C ?
Yes
A, B, C, F ? No
H, G, F, E ?
Yes
E, H, C, B ?
Yes
A, G, F ?
Yes
C, B, F, H ? No
Lesson 1-1 Point, Line, Plane

17. Line Segment (or segment)
A section of a line that has 2 endpoints
Named by its endpoints. AB or BA A B

18. Ray
Piece of a line with only one endpoint (initial point) and continues forever in the other direction
Named by the endpoint and a second point named on the ray. (name MUST begin with the endpoint!) AB A B

19. NAMING A RAY

20. Opposite Rays QP and QS are opposite rays.
2 rays that share a common initial point and face opposite directions.
QP and QS are opposite rays. P Q S

21. A. Name 4 points in the figure.
B. Name the two lines in the figure.
C. Name the plane in the figure.
D. Name four segments in the figure.
E. Name four rays in the figure.

22. Postulate or axiom– an accepted statement of fact.
Lines k and l have point A in common, so point A is the intersection
Two planes intersect in a line

23. INTERSECTING PLANES CG Name the intersection of each pair of planes CB
Plane ABC and CGF CB
Plane DHA and EHF HE
Plane ABF and FGH EF
Plane CBF and DHC CG

24. CLASSWORK PRACTICE
Textbook: PAGE 16 #8-24

25. The End

26. Modeling Activity

27. Activity Questions
1. When the cards are NOT together: What is the intersection of AB and CD? AB and EF? 2. With the cards together, what is the intersection of CD and EF? 3. What is the intersection of planes M and N? 4. Are CD and EF coplanar? Explain.