1. Warm-up

2. Agenda Learn about famous books Begin Chapter 1
Review Coordinate Plane
Discover Basic Building Blocks
Points, Lines, & Planes
Bring book tomorrow (Thursday)

3. Books… The Elements Euclid 300 BC Required reading for 2000 years
Over 1000 editions
Most popular textbook

4. More books… Flatland Flatterland Edwin Abbott Abbott 1884 novella
Satire on Victorian Society
Primer for school geometry
Flatterland
Ian Stewart
2001
Flatland – 0 to 3 dimensions – Euclidean Geometry
Edwin A Abbott – Headmaster
1884
Flatterland – Euclidean & Non-Euclidean, Physics
Ian Stewart
2001

5. 1-1 Coordinate Plane II I IV III Quadrants y-axis Ordered Pair
(x-coordinate, y-coordinate)
(2, 3) II I
y-axis
Chapter 1
Section 1-1
Coordinate Plane (What is missing? Arrows)
x-axis, y-axis, Origin
Point - (1,2) - (x coordinate, y coordinate) - Ordered Pair
Two Points (1,2) (4,4) - Line
Quadrants
I (+,+)
II (-,+)
III (-,-)
IV (+,-)
What popular kid’s game uses two coordinate planes? (Battleship)
x-axis IV
III

6. Determine Coordinates
Point Quadrant
O ( 0 , 0 ) Origin
P ( 2 , -5 ) IV
Q ( -3 , -4 ) III
R ( 0 , -2 ) y-axis O
Plot points and have students determine their coordinates.
O (0,0) Origin
P (2, -5) IV
Q (-3,-4) III
R (0,-2) y-axis R Q P

7. What do you see? X Y A B C (0,4) -4 -2 -8/3 4 2 7 (-8/3, 0)4 2 7
(-8/3, 0)
What can you tell me about these three objects?
All represent the same set of data points.

8. Collinear/Noncollinear
Plot three points, connect
Add fourth point, not on line
Draw second line connecting fourth point to one point on line, now they are collinear B D A

9. Answers Ahead

10. Study Guide 1-1

11. Section 1-2 Points P Basic building block Zero dimension (no size)
Named with a capital letter
Draw point A
Draw point B
Flatland – lonely, isolated objects P

12. Lines m Continuous set of points One dimension (length)
Named with a lower case script letter or by two points on the line
Draw points A and B, make line AB (remember arrows), name it lower case script m
(arrows indicate line extends indefinitely)
Show possible names line AB, line BA, AB (under arrow), BA (under arrow)
Draw line with points R, S, T, U (Flatland – points only know neighbor)
12 possible names RS, RT, RU, ST, SU, TU, UT, US, UR, TS, TR, SR (under arrows)
Why doesn’t it matter what you name it?
Line segment – distance from one point to another
Named with two points under a straight line B m A

13. Plane Continuous points, multiple lines Two dimensions (length, width)
Named with a capital (uppercase) script letter S
Draw plane with noncollinear points P, Q, S – name it R
Points are coplaner, some points with also be collinear
Much richer environment, many 2D shapes P R Q

14. Point, Line, Plane Undefined terms in Geometry
Can use examples and descriptions to define but not rigorous mathematics
Terms are used to define more complex geometric terms, shapes and properties

15. Some basic rules
A point can be on multiple lines and planes P l m

16. Intersecting lines
Two lines intersect at one point, no points or all points p
The intersection of two figures is the set of points that are contained in both figures.
Both lines contain point T.
Draw Point A, show multiple lines, plane
Show following slide
Add parallel line
Add coincident line
Show third slide n

17. Lines and Planes
A line can intersect a plane or be contained within a plane
A line intersects a plane at a single point
Point R on line m and plane N.
All of l is contained by plane N

18. Intersecting Planes Two planes intersect at a line
Line AB is on planes P and Q.

19. Points, lines & planes
Line AB is on planes P and Q.

20. Points, lines & planes
Line AB is on planes P and Q.

21. Points, lines & planes
Line AB is on planes P and Q.

22. Points, lines & planes
Line AB is on planes P and Q.

23. Points, lines & planes
Line AB is on planes P and Q.

24. Answers Ahead

25. Study Guide 1-2

26. Study Guide 1-2

27. Homework Define point, line and plane in your own words.
Finish Study Guides, Practice pages
Section 1-1
Section 1-2