1. Create two [b]points A[/b] and [b]B[/b] using the [b]Point Tool[/b].[br][i]Note: GeoGebra should label the points automatically. You may rename the points by double clicking on the point.[/i][br][br]2. Create a [b]line[/b] through [b]points A[/b] and [b]B[/b] using the [b]Line Tool[/b].
How many lines can you create that go through both points A and B?
one[br][br][i][b]Unique Line Postulate[/b]: Through any two points there exists one and only one line.[/i]
How many points are needed to create a line?
two[br][br][i][b]Point Existence Postulate for Lines[/b]: A line contains at least two points.[/i]
3. Using the [b]Line Tool[/b], create [b]line CD[/b] with[b] point D[/b] lying on [b]line AB[/b].[br]
What is the intersection of these two lines?
point D[br][br][i]If two distinct lines intersect, then they intersect at one and only one point.[/i]
1. Use the [b]Point Tool[/b] to create three [b]points [/b]([b]A[/b],[b] B[/b], and[b] C[/b]).[br][br]2. Use the [b]Plane Tool[/b] to create a [b]plane [/b]through [b]points A[/b],[b] B[/b], and[b] C[/b].
How many points are needed to create a plane?
three[br][br][i][b]Point Existence Postulate for Planes[/b]: A plane contains at least three noncollinear points.[/i]
How many planes can be created through three noncollinear points?
one[br][br][i][b]Unique Plane Postulate[/b]: Through any three noncollinear points there exists one and only one plane.[/i]
3. Use the [b]Point Tool[/b] to create [b]Point D [/b]on the [b]plane[/b].[br][br]4. Use the [b]Attach/Detach Point Tool[/b] to move [b]point D[/b] above or below the plane.[br][br]5. Use the [b]Line Tool[/b] to create [b]line AB[/b].
Is [b]line AB[/b] located on [b]plane ABC[/b]?
Yes[br][br][i][b]Flat Plane Postulate[/b]: If two points are in a plane, then the line that contains those points lies entirely in that plane.[/i]
6. Use the [b]Plane Tool[/b] to create a [b]plane[/b] through [b]Points A[/b],[b] B[/b], and[b] D[/b].
Is [b]line AB[/b] located on [b]plane ABD[/b]?
Yes[br][br][i][b]Flat Plane Postulate[/b]: If two points are in a plane, then the line that contains those points lies entirely in that plane.[/i]
What is the [b]intersection[/b] of [b]plane ABC[/b] and [b]plane ABD[/b]?
line AB or line BA[br][br][i]If two planes intersect, then their intersection is a line.[/i]
7. Use the [b]Line Tool[/b] to create [b]line CD[/b].
Does [b]line CD[/b] lie in [b]plane ABC[/b]?
No, it intersects the plane at point C.[br][br][i]If a plane and a line intersect, they intersect at one point.[/i]
Where does [b]line CD[/b] intersect [b]plane ABD[/b]?
at point D[br][br][i]If a plane and a line intersect, they intersect at one point.[/i]