Question

Consider the words typically associated with geometry. Are there any words that would be hard to precisely define? What words can you think of?

Answer 1

Words that are not typically defined in geometry are:

Point, line and plane.

Step-by-step explanation:

Words are defined using other defined words or terms. However, these three terms are very difficult to find other words to describe. Without using other terms, we create circular definitions; thus these are called the "undefined terms" of geometry.

Answer 2

In geometry, we have many formal definitions using defined words or terms. However, I can think of three words that are not formally defined. These words are point, line and plane. Even though these words are undefined we can describes them as follows:

1. Point. A point is an exact position or location in space.
It is important to understand that a point has no dimension (that is, actual size). So, it has no length, no width, and no height (thickness).
We usually named a point with a capital letter. In the coordinate plane, a point is named by an ordered pair,
`(x,y)`.
Even though we represent a point with a dot, the dot can be very tiny or very large. Recall that a point has no size.

2. Line (Straight line)

A line has no thickness.
So, its length extends in one dimension.
The line extends in both directions without end (infinitely). A line has infinite length and has no width, no height.
We assume the line to be straight.
and can be drawn with arrowheads on both ends.

3. Plane

A plane is a flat surface with no thickness extending indefinitely in all directions and having two dimensions. So, it has infinite length, infinite width and has no height (thickness). Moreover, a plane is drawn as a four-sided figure resembling a parallelogram.

The representation of each concept is shown in the Figure below.