Question

name ____ date ____
lesson 1.1 practice continued
for use with the lesson \identify points, lines, and planes\

1. counter stools two different types of stools are shown below.

a. one stool rocks slightly from side to side on your kitchen floor.
which of the two stools could this possibly be? explain why this might
occur.
images: three - legged stool, four - legged stool
b. suppose that each stool is placed on
a flat surface that is slightly sloped.
do you expect either of the stools to
rock from side to side? explain why
or why not.

Explanation:

Part (a)

In geometry, three non - collinear points define a unique plane. A three - legged stool has its three legs (the points where it touches the floor) defining a plane, so it is stable. A four - legged stool has four legs. If the kitchen floor is not perfectly flat (i.e., the four points where the legs touch the floor are not coplanar), the stool will rock as it tries to find a stable position where all four legs touch the floor (or as many as possible), since four points do not always lie on a single plane, and the stool will adjust to balance, causing the rocking motion.

Part (b)

For the three - legged stool: Since three non - collinear points always lie on a single plane, even on a sloped surface, the three legs will rest on the sloped plane (the surface) without rocking. For the four - legged stool: A sloped surface is still a plane. But the four legs of the stool may not all lie on this sloped plane (because four points are not guaranteed to be coplanar). So the four - legged stool will try to balance, and this can result in a rocking motion as it adjusts to have as many legs as possible on the sloped surface.

Answer:

The four - legged stool.