What are the two undefined geometric terms?

In geometry, formal definitions are formed using other defined words or terms. There are, however, three words in geometry that are not formally defined. These words are point, line and plane, and are referred to as the "three undefined terms of geometry". Índice Show Undefined Terms in Geometry (Video & Examples) What you'll learn: Undefined Terms Definition Undefined Terms Examples Lesson Summary Next Lesson: What are the undefined terms in geometric? What are the 3 undefined terms give two examples in every undefined term? How many undefined terms are there in geometry? Which is an example of undefined and defined terms? While these words are "undefined" in the formal sense, we can still "describe" these words. The descriptions, stated below, refer to these words in relation to geometry. POINT • a point indicates a location (or position) in space. • a point has no dimension (actual size).  • a point has no length, no width, and no height (thickness). • a point is usually named with a capital letter. • in the coordinate plane, a point is named by an ordered pair, (x,y). While we represent a point with a dot, the dot can be very tiny or very large. Remember, a point has no size. The size of the dot drawn to represent a point makes no difference. Points have no size. They simply represent a location. LINE (straight line) • a line has no thickness.  • a line's length extends in one dimension. • a line goes on forever in both directions. • a line has infinite length, zero width, and zero height. • a line is assumed to be straight. • a line is drawn with arrowheads on both ends. • a line is named by a single lowercase script letter, or by any two (or more) points which lie on the line. Lines can be labeled with a single script letter, or by two points on the line, . The thickness of a line makes no difference. PLANE • a plane has two dimensions. • a plane forms a flat surface extending indefinitely in all directions. • a plane has infinite length, infinite width and zero height (thickness). • a plane is drawn as a four-sided figure resembling a tabletop or a parallelogram. • a plane is named by a single letter (plane m) or by three coplanar, but non-collinear,* points (plane ABC). Plane m or Plane ABC. While the diagram of a plane has edges, you must remember that the plane actually has no boundaries. * Collinear points are points that lie on the same straight line. Coplanar points are points that line in the same plane. NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation and is not considered "fair use" for educators. Please read the "Terms of Use".

Undefined Terms in Geometry (Video & Examples)

Video Definition Point Line Plane Set Examples

A certain famous, fictional spy always describes his favorite beverage as "shaken and not stirred." Four concepts in geometry can best be thought of as "described and not defined."

What you'll learn:

After working your way through this lesson and video, you will be able to:

• Identify and describe the three undefined terms -- point, line, plane -- of Euclidean geometry
• Identify and describe the undefined term, set, used in geometry and set theory

Undefined Terms Definition

In all branches of mathematics, some fundamental pieces cannot be defined, because they are used to define other, more complex pieces. In geometry, three undefined terms are the underpinnings of Euclidean geometry:

1. Point
2. Line
3. Plane

A fourth undefined term, set, is used in both geometry and set theory.

Even though these four terms are undefined, they can still be described. Mathematicians use descriptions of these four terms and work up from them, creating entire worlds of ideas like angles, polygons, Platonic solids, Cartesian graphs, and more.

Simply because these terms are formally undefined does not mean they are any less useful or valid than other terms that emerge from them. These four undefined terms are used extensively in theorems, proofs, and defining other words.

Point

A point in geometry is described (but not defined) as a dimensionless location in space. A point has no width, depth, length, thickness -- no dimension at all. It is named with a capital letter: Point A; Point B; and so on.

Points in geometry are more like signal buoys on the vast, infinite ocean of geometric space than they are actual things. They tell you where a spot is, but are not the spot itself (even though we show them with a dot).

When you place two points on a plane, you can create a line.

Line

A line is described (not defined) as the set of all collinear points between and extending beyond two given points. A line goes out infinitely past both points, but in geometry we symbolize this by drawing a short line segment, putting arrowheads on either end, and labeling two points on it. The line is then identified by those two points. It can also be identified with a lowercase letter.

With only three points, you can create three different lines, and you can also describe a plane.

Plane

A plane is described as a flat surface with infinite length and width, but no thickness. It cannot be defined. A plane is formed by three points. For every three points in space, a unique plane exists.

A symbol of a plane in geometry is usually a trapezoid, to appear three-dimensional and understood to be infinitely wide and long. A single capital letter, or it can be named by three points drawn on it.

Modeling a plane in everyday life is tricky. Nothing will accurately substitute for a plane, because even the thinnest piece of paper, cookie sheet, or playing card still has some thickness. Also, all of these objects end abruptly at their edges. Planes do not end, and they have no thickness.

Set

A set can be described as a collection of objects, in no particular order, that you are studying or mathematically manipulating. Sets can be all these things:

• Physical objects like angles, rays, triangles, or circles
• Numbers, like all positive even integers; proper fractions; or decimals smaller than 0.001
• Other sets, like the set of all even numbers and the set of all multiples of five; the set of all acute angles and the set of all angles less than 15°

In geometry, we use sets to group numbers or items together to form a single unit, like all the triangles on a plane or all the straight angles on a coordinate grid. Sets are shown by using braces, { } on either side of the set:

• { 0.1, 0.2, 0.3 } for a set of three decimal numbers
• { 1, 2, 4, 8, 16 … } for the infinite set of powers of two
• {acute angles, obtuse angles, reflex angles, straight angles} for a set of angles found in plane geometry
• { 1, 2, 3 … } for the infinite set of whole positive integers
• { A, B, C … X, Y, Z } for the set of English alphabet letters

A set does not need to have a limit. The ellipsis ( … ) can indicate more terms between the start and end of the series, or it can indicate that the set between the braces continues on, infinitely.

A set does not need to ordered, like an array. You can write the first two sets shown above like this:

• { 0.2, 0.1, 0.3 } or like this { 0.3, 0.2, 0.1 }
• { 4, 8, 16, 1, 2 … } or like this { 16, 2, 4, 1, 8 ... }

Undefined Terms Examples

Look on the floor of your bedroom. Mentally arrange a set of what you see. It might look like this:

• { socks, gym shorts, left shoe, geometry textbook }

Look at a calendar. Mentally (or, better, jot down) a set of Saturday and Sunday dates. It might look like this:

• { 13, 14, 6, 20, 7, 27, 21, 28 }

The order does not matter, but the set might be easier to work with in order from least to greatest:

• { 6, 7, 13, 14, 20, 21, 27, 28 }

Lesson Summary

Now that you have navigated your way through this lesson, you are able to identify and describe three undefined terms (point, line, and plane) that form the foundation of Euclidean geometry. You can also identify and describe the undefined term, set, used in geometry and set theory.

Next Lesson:

Geometric Figures

What are the undefined terms in geometric?

What are the 3 undefined terms give two examples in every undefined term?

How many undefined terms are there in geometry?

Which is an example of undefined and defined terms?