# Geometry Notes 1.1: Points,Lines, and Planes

Undefined terms: A point is a location and is named by a capital letter. A line is made up of points and has no thickness or width. It is named with two letters representing points on the line, or a lowercase script letter. A plane is an infinite flat surface made up of points and is named by a capital script letter or by three letters representing non collinear points on a plane. Collinear points can be contained on a line. Coplanar points can be contained on a plane.
FIRST DIAGRAM: Drag the diagram around by moving the points (you can even make it spin!), and then wait for the class.
BREAK OUT ROOMS: remember to leave your microphone on, and talk through the problems with your partner. Compare answers, and discuss what you see. Do #1 - #4 on GeoGebra, and #1-#4 on your printed notes.

1. Name 3 collinear points

2. Name 3 noncollinear points:

3. Name a plane.

4. Name in a different way. (Choose all that apply)

Select all that apply
• A
• B
• C
• D
Now do #1-#4 on your printed notes together, and then: STOP! LEAVE YOUR BREAK-OUT ROOM AND GO BACK TO THE MAIN ROOM! (Don't do #5 yet.)
Next: With the teacher: Draw , ( ) and then drag it. Notice how the part of the line that is behind the plane is dashed. Draw plane CEA ( ), and then drag it. Then delete the line and plane that you drew.
BREAK OUT ROOMS: remember to leave your microphone on, and talk through the problems with your partner. Compare answers, and discuss what you see. Do #5 - #12 on GeoGebra, and then do # 5 - #10 on your printed notes.

5. If possible, draw a line through E and C. Are E and C collinear?

Select all that apply
• A
• B

6. If possible, draw a line through E, G, and C. Are E, G, and C collinear?

Select all that apply
• A
• B

7. If possible, name two points that are non collinear, because you CANNOT draw a line through them.

8. If possible, draw a plane through D, B, and F. Are D, B, and F coplanar?

9. If possible, draw a plane through A, G, E, and B. Move the diagram around to see if the four points are on the plane. Are A, G, E, and B coplanar?

10. If possible, name 3 points that are NOT coplanar, because you CANNOT draw a plane through them.

SECOND DIAGRAM: Use points F, D, and E to drag the rectangular prism around. Then answer the following questions. Remember to discuss each problem with your partner-- microphones on, talk over the question.

11. Name the intersection of and .

12. Name the intersection of and (the lines are not shown)

Do #5 - #10 on your printed notes together, and then: Stop! Leave the breakout room and go to the main room.(Don't do #16 yet.)
Next we will practice drawing a 3 dimensional diagram in two dimensions, as though you are drawing on paper. How can you represent a plane? How can you represent a line or point that is NOT on that plane? First, practice with the teacher: a) Draw a plane that looks like the plane in the printed notes. ( using the polygon tool. ( ) b) Draw two points on the plane, and draw the line through them. ( and ) c) Draw two points NOT on the plane, draw the line through them. ( and ) d) Use dashed segments to make it clear that that line is not on the plane. ( )

## Try #16 on your own:

16. Use the Applet below. a) Draw two points, P and Q using the tool. b) Sketch using the tool. c) Add a point R on the line so that Q is between P and R.

## Try #17 on your own, except for d).

17. Use the Applet below. a) Draw a plane using the tool. b) Put point Q on the plane using the tool. c) Draw ﻿ so that it intersects the plane only once. d) We can use the segment tool to do a pretty good job of creating a dashed section. ## Drawing a 3D diagram in two dimensions!

Now let's finish the PRINTED NOTES. Don't log off GeoGebra yet, though.