"El punto, la línea y el plano son los elementos fundamentales de la composición." (Kandinsky, 1922)
Many Primary students begin geometry directly with figures like the triangle or square, without understanding the most basic elements on which they are built: the point, the line and the plane. This post will help you to visually and meaningfully understand these concepts.
The point: origin of all geometric construction
The point is the most basic unit in geometry. It is characterized by:
- It has no length, width or volume.
- Represents a position in space and is usually denoted by capital letters, such as A, B or C.
There are two types of points:
- Collinear: those that are on the same line.
- Coplanars: those that are contained in the same plane.
The concept of point is fundamental, since it serves as a reference to define other geometric elements.
The straight line: an infinite succession of points
A line is made up of an infinite number of aligned points. It has only one dimension: length.
A single line passes through two different points, which means that with only two points we can determine a straight line.
Straight lines are classified in:
- Parallel: they are on the same plane and do not intersect.
- Perpendicular: intersecting at right angles.
- Oblique: intersecting at angles that are not straight.
A segment is a part of a straight line bounded by two points, called ends.
The plane: the two-dimensional space
The plane is a two-dimensional surface that extends infinitely in all directions. It is formed by an infinite number of points and lines. Although it has no volume, it has length and width.
A plane can be defined in several ways:
- For three unaligned points.
- For a straight line and a point that does not belong to it.
- By two intersecting straight lines.
In teaching, the plane is commonly represented as a sheet of paper or chalkboard, making it easier to understand more complex concepts such as geometric figures and coordinates.
Geometry and everyday life: where do we see points, lines and planes?
Geometry does not live in books: it is everywhere. Bringing these concepts to the everyday world
makes learning meaningful.
The point in real life:
- A lift button.
- A pin on a map.
- The location marker in Google Maps.
The line in real life:
- The edge of a table.
- The light cables that hang tight.
- The railway tracks.
- A rope stretched between two trees.
The plane in real life:
- The floor of a room.
- The surface of a sheet or touch screen.
- A glass window.
- The wall where we hang a picture.
🎲Review Activity
Here I leave you an activity designed by me in which you can test your knowledge on this subject. You just have to click on the image and it will open the activity directly
Let’s go! ⤵️
Finally, so that you can review everything we have seen today, I leave you a video that explains everything, if you have any doubts!
See you in the next geometric adventure!🧩
Bye!
References:
Matarozzo, E. (2021). El punto, la recta y el plano. Billiken. https://billiken.lat/para-tus-tareas/el-punto-la-recta-y-el-plano/
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