Point, Line, and Plane Postulates and Properties
Exploration 1
Exploration 1
1. Create two points A and B using the Point Tool.
Note: GeoGebra should label the points automatically. You may rename the points by double clicking on the point.
2. Create a line through points A and B using the Line Tool.
How many lines can you create that go through both points A and B?
How many points are needed to create a line?
3. Using the Line Tool, create line CD with point D lying on line AB.
What is the intersection of these two lines?
Exploration 2
Exploration 2
1. Use the Point Tool to create three points (A, B, and C).
2. Use the Plane Tool to create a plane through points A, B, and C.
How many points are needed to create a plane?
How many planes can be created through three noncollinear points?
3. Use the Point Tool to create Point D on the plane.
4. Use the Attach/Detach Point Tool to move point D above or below the plane.
5. Use the Line Tool to create line AB.
Is line AB located on plane ABC?
6. Use the Plane Tool to create a plane through Points A, B, and D.
Is line AB located on plane ABD?
What is the intersection of plane ABC and plane ABD?
7. Use the Line Tool to create line CD.
Does line CD lie in plane ABC?
Where does line CD intersect plane ABD?