You will get to learn what planes areand how they relate to lines and points.
After completing this tutorial, you will be able to complete the following:
What is the definition of a plane? How do we represent and name planes?
~ A plane is a flat object that extends infinitely along its edges, but has no thickness. We typically represent planes with a parallelogram and name them with capital letters.
What are some examples of physical objects that can be modeled by planes? What do we call these objects?
~ Answers may vary. The surface of walls, floors, windows, and tabletops can be thought of as parts of a plane. We call such objects planar figures or planar surfaces.
What are some ways to form a plane?
~ The Animation describes four ways to form a plane:
1. Any three non-collinear points determine a plane.
2. A line and a point outside this line determine a plane.
3. Two parallel lines determine a plane.
4. Two intersecting lines determine a plane.
Notice that 2-4 are all special examples of 1.
Can you think of an explanation for why a stool or table with three legs will never wobble, while a stool or table with more than three legs might wobble?
~ Answers may vary. The points at the ends of the legs of a three-legged stool or table determine exactly one plane. For this reason, when a three-legged stool or table is placed on a planar surface, such as the floor, it will always sit flat. When a table or stool has more than three legs, the points at the ends of any three of the legs will determine a single plane, but different combinations of legs may determine different planes. When placed on a planar surface, such as the floor, a table or stool with more than three legs will wobble as different combinations of its legs determine different planes.
|Approximate Time||2 Minutes|
|Pre-requisite Concepts||Students should be able to define a 2-dimensional shape, collinear points, and coincident lines.|
|Type of Tutorial||Animation|
|Key Vocabulary||non-collinear points, non-coincident lines, line|