The types of lines as part of geometry
Lines are a base element within geometry. It can be of different types depending on different factors. For example of its relationship in the plane or in space with another line. Or depending on the inclination they have in the plane or in space. Thus we can speak of parallel and perpendicular lines and even intersecting lines. But we can also refer to lines depending on the position they occupy in space. Being vertical, horizontal or oblique. There are also many more variations. Think about number lines and even number lines with fractions. As you can see the world of straight lines encompasses many possibilities.
In this article we are going to talk about the types of lines. So you know how to differentiate one from the other easily. You will know all the information about the types of lines in a generic way. If you want to learn more specific information about each type of line, we advise you to take a look at the last section of this article. In it you will find references to other longer articles on each type of line. We are sure that they will help you to learn more about the interesting world of geometry. Are you ready to learn everything about the types of lines? In that case, keep reading!
All the information about the types of lines
What is a line?
Before knowing all the types of lines, it is important to know what a line is. The line is one of the basic elements that geometry studies along with planes or points.
- The main characteristic of the line is that it is made up of many very small points that always move towards the same direction and in a single dimension. If we looked at a line with a magnifying glass, we would realize that it is made up of many points. However, when seeing it from afar, it gives us the sensation of finding ourselves before a line.
- The composition of points generated by the line is infinite. It has no beginning or end.
Many people confuse lines with:
- Rays, composed of a start point but no end point.
- The segments. Line segments are parts of a line made up of a start point and an end point.
This confusion is usually related to the way of explaining geometry. When teachers explain the concept of a line, they draw a line on the board. This line really has a beginning and an end, so it’s actually a segment. You have to extrapolate with this explanation and imagine that this line never ends so as not to confuse it with the segments or the rays.
Types of lines according to their position in a plane
Lines receive different names depending on their position on a plane or even in space. The types of lines that we can find in this case are the following:
- Horizontal lines. If you pay attention, we observe the world around us horizontally. The largest horizontal line that you can see day after day is the horizon. When you look at the sea this line is clearly seen. Well, this is precisely the position that lines acquire when they are horizontal. As if they are lying how long they are.
- Vertical lines. We can also see vertical shapes around us. If you look at a lamppost you will see that it extends from the bottom to the top in a very straight line. This image corresponds to that of vertical lines. Do you know what is also vertical? The imaginary line that joins the poles of the earth on a plane.
- Oblique lines. Not all lines acquire a horizontal or vertical position. Some have a bit of a weird angle. This is the case of oblique lines. Can you think of a well-known monument whose shape resembles an oblique line? That’s it! The tower of Pisa.
We now know that lines can be horizontal, vertical, or oblique. But what happens if there are more lines in the same plane? Imagine two lines in the same plane. These can acquire different positions. And depending on those positions they will receive one name or another. Depending on the position between them, the lines are called differently. Let’s see it next.
- Parallel lines. Parallel lines are considered to be those lines that advance in the same direction and have the same inclination to each other. Furthermore, these lines meet each other at the same distance. Can you think of any everyday element where you can find parallel lines? Look at the train tracks. They always advance with the same slope and in the same direction. Parallel lines, in turn, can have different properties. Let’s imagine that there are several lines to understand it well. Thus they can be:
- Symmetrical parallel lines. To understand it, try to answer the following question. If line A is parallel to line B, is line B parallel to line A? Indeed. For this reason it is said that these lines have symmetric properties.
- Reflexive parallel lines. We know that parallel lines are symmetric. That is, if A is parallel to B, B is parallel to line A. Therefore they also have reflective properties.
- Transitive parallel lines. Now imagine that there are three lines in the same plane. A, B, and C. If they are symmetrical and reflexive, will A and C be parallel to each other just as B and C are? Indeed, they have the property of being transitive. They are all parallel to each other. We know that for the lines to be parallel they must all point in the same direction. It is another of its properties. Well, this property is called a corollary.
- Perpendicular straight lines. Perpendicular lines are those that intersect at a point. From this cut, 4 right or 90º angles are created. For them to be perpendicular it is necessary that right angles be generated. Otherwise they would not be perpendicular but intersecting. Can you think of an image that makes up perpendicular lines? The cross of Christians! If you look at the blades of the cross, they are cut forming 4 90º angles. The X symbol also intersects forming 4 right angles.
- Secant lines. It is considered that a straight line is intersecting when there is at least one point in common when intersecting them. These straight lines can cut another straight line at a single point or they can cut a curve at two points. The secant lines, therefore, are all those that intersect or intersect. Perpendicular lines are also intersecting. However, not all secants are perpendicular. Think that the lines can be cut creating different types of angles. They do not have to be 90º. If they are cut creating angles that are not 90º, they will be intersecting but not perpendicular.
- Tangent lines. Lines can also be tangent to another shape. This happens with curves. When a line touches a curve but does not intersect it, this relationship is known as a tangent. It’s as if he touched her from the side but didn’t get inside her. Imagine a circus tightrope walker on a bicycle advancing along the rope. The string would be a tangent line that would only touch the wheel, but would not intersect it in any case.
Let’s do some exercises about the types of lines
Ok, we have already talked about the different types of lines depending on their position in a plane and depending on their position between them. We know that they can be tangent, secant, perpendicular, or parallel. We know that they can be upright, horizontal or oblique. But, have we really understood what each of these lines are like? Let’s check it with the following visual exercises. You can see the solution a few lines below.
Exercises on types of lines
- Exercise 1. María and Juanito want to go to the park. They love swinging on the swings. It is undoubtedly one of his favorite pastimes. This afternoon her grandmother has decided to bring them closer even though it’s a bit cold outside. Since the weather is not very good and there is some air, her grandmother has decided to play with them so they can learn new things. And her challenge has been for the children to find out what kind of lines the chains of the swings form with each other. Could you tell us?
- Exercise 2. Jose is passionate about cars. At eight years old, he dreams of being able to drive an SUV through the desert and reach places where no one has yet been. Another thing that he loves are the roads. With its beautiful shapes and its lines that seem to never end. These lines always maintain the same slope and move together in the same direction. Can you tell what kind of lines they are?
- Exercise 3. Parking lots at night can be scary. They are dark and gloomy places where there is not a single parked car. Juan has always been a bit scared. That is why his sister Lucía de él has decided to downplay the matter by posing a riddle. If you look at the squares of the cars they cut each other forming right angles. One after another. Do you know what kind of relationship these lines have with each other?
Solutions on types of lines
- Solution to exercise 1. It is clear that swings are one of the most fun elements in playgrounds. But since that day María and Juanito could not go up to swing because of the cold, her grandmother had a great idea. Find out what kind of lines the chains form. Have you found out too? They are parallel lines.
- Solution to exercise 2. Cars can be a lot of fun. Just like the motorcycles. But geometry is not far behind. Highways, just like train tracks, form parallel lines. All its points always move towards the same direction and distance.
- Solution to exercise 3. In this case, it is about perpendicular lines.