[color=#3c78d8]Undefined terms: [br]A [b]point[/b] is a location and is named by a capital letter.[br]A [b]line [/b]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.[br]A [b]plane[/b] 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.[br][b]Collinear[/b] points can be contained on a line.[br][b]Coplanar [/b]points can be contained on a plane.[/color]
[size=150][size=200]FIRST DIAGRAM: Drag the diagram around by moving the points (you can even make it spin!).[/size][/size]
1. Name 3 collinear points. (Turn the diagram if needed)
B, A, C[br][br](note: did you write capital letters? did you use commas?)
2. Name 3 noncollinear points:
Many correct answers![br]Here is one: A, D, G
4. Name [math]\text{\overleftrightarrow{AB}}[/math] in a different way. (Choose all that apply)
[br]5. Draw [math]\text{\overleftrightarrow{BD}}[/math], ([icon]/images/ggb/toolbar/mode_join.png[/icon]) and then drag it. Notice how the part of the line that is behind the plane is dashed.[br]Draw plane CEA ([icon]/images/ggb/toolbar/mode_planethreepoint.png[/icon]), and then drag it.[br]Then delete the line and plane that you drew.[br][br]
6. If possible, draw a line through E and C. Are E and C collinear?
7. If possible, draw a line through E, G, and C. Are E, G, and C collinear?
8. If possible, name two points that are non collinear, because you CANNOT draw a line through them.
Not possible.[br]We say:[br]Through any two points there exists a line.[br]or:[br]Two points determine a line.
9. If possible, draw a plane through D, B, and F. Are D, B, and F coplanar?
10. 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?
No. (not possible to draw a plane, because A, G, E, and B are not coplanar.)
11. If possible, name 3 points that are NOT coplanar, because you CANNOT draw a plane through them.
Not possible.[br]We say:[br]Through any 3 points exists a plane.[br]or:[br]Three points determine a plane.
SECOND DIAGRAM: Use points F, D, and E to drag the rectangular prism around. Then answer the following questions.
12. Name the intersection of [math]\text{\overline{FA}}[/math] and [math]\text{\overline{AE}}[/math].
13. How many planes are in the image?
15. Name two planes that do not intersect.
(Several solutions)[br]plane ABG and plane FED[br][br]