ZingPath: Planes and Angles

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.