Lines are part of geometry. In fact, together with the plane and the point, they are basic elements of this branch of mathematics. Within the types of lines, oblique lines are quite common. Some people, however, show some difficulty in recognizing this type of lines. If you are starting to investigate the interesting world of lines, you have come to the right place. For this we are going to offer you a detailed explanation of this concept. Also, since a picture is worth a thousand words, we propose a game. At the end of the article we are going to challenge you to solve some visual exercises to see if you have truly understood what we have explained to you. Would you like to continue learning more about oblique lines, what they are and what they mean? In that case, be sure to read the following post. Let’s get started!
What are oblique lines? Its meaning
Before explaining this term, the first thing we have to look at is its composition. If you realize it is made up of two words “straight” and “oblique”. Let us explain its meaning before continuing.
What are the lines?
Lines are one of the basic elements of geometry. Geometry, in turn, is one of the best-known branches of mathematics. Lines are one-dimensional elements made up of many small points. The point, along with the plane and the line, are basic elements in geometry.
If you were to approach a straight line with a magnifying glass, you would realize that it is made up of many tiny dots. When we see these points from afar, we have the sensation of seeing a line. The lines are characterized by:
- Be one dimensional.
- Be made up of points that always move in the same direction.
- Be infinite.
- Lack of beginning and end.
Many people confuse lines with rays or segments. However, they are not the same concepts.
- The half lines. These types of straight lines are characterized by having an initial point but lacking an end point.
- The segments. Segments are parts of a line since they have a beginning and an end.
These confusions usually appear due to the way in which these forms are represented while we study them. To represent a straight line, what teachers do is draw a line on the blackboard. This line has a beginning and an end. Then it is a segment. However, we cannot paint something infinite, so teachers use this shape to explain what lines are like. You have to be careful and always remember that straight lines never end or begin.
What does the term oblique mean?
When we speak of something oblique, we refer to the position it occupies on the plane or in space. This position implies that the object or element is tilted.
Therefore, when we refer to oblique lines we are thinking of lines that have a natural inclination.
Oblique lines are part of secant lines. We know that intersecting lines are those that intersect a line or a curve at some point. It is necessary that they have that point in common to be drying. Otherwise they would be parallel lines. Intersecting lines can also cut a curve at two different points.
Depending on the inclination that the secant lines have when cut, they can be perpendicular or oblique.
- Perpendicular secant lines. Perpendicular secant lines are those that when intersected create four 90º angles. That is, right angles.
- Oblique secant lines. Oblique intersecting lines, however, do not create right angles. When they cut each other they create angles but not 90º.
Although perpendicular lines and oblique lines are intersecting at the same time they are exclusive. What does this mean? That if a line is perpendicular it cannot be oblique. And the same thing happens against it. That is, if a line is oblique it cannot be perpendicular. However, what can happen is that the relationship between several lines is oblique and perpendicular at the same time. For example, line A can be perpendicular to line B. And in turn, line A can be oblique to line C. You can see an example in the following image.
So that you understand it more easily, we are going to explain some of its characteristics below:
- Oblique lines are considered to be those lines that are inclined in the plane or in space.
- They are also oblique lines depending on the relationship they have with other lines. For them to be oblique it is necessary:
- That they cut another line at some point and that, in doing so, generate angles that are not right. In this case we would say that it is oblique to the line.
- When a line on a plane is neither parallel nor perpendicular in its position, then it is oblique.
For a line to be oblique it is necessary that:
- Be leaning.
- When intersecting with other lines, it does not create 90º angles. Or what is the same, right angles.
- That generate angles when intersecting with other straight lines of more than 90º. That is, obtuse angles.
- That generate angles when intersecting with other lines of less than 90º. That is, acute angles.
- When intersecting with other lines they generate angles that are not equal.
- They are represented in the form of
Properties of oblique lines
Oblique lines are characterized by fulfilling a series of properties. Let’s look at these properties below to understand them a little better:
- Oblique straight lines start at different points. And they do it independently. However they end up cutting each other at one point. And when they are cut they create angles that are not right. If they were 90º angles they would be perpendicular lines.
- When from an exterior point several obliques are drawn to the perpendicular line:
- If the obliques that are drawn have the same distance from the foot of the perpendicular line, they are all equal to each other.
- In the event that the obliques do not have the same distance from the foot… In this case, the one that is furthest from the foot of the perpendicular line is the largest of the oblique lines.
- The perpendicular will always be less than any of the other obliques that have been drawn.
Some exercises with oblique lines
Now that we know what oblique lines are, the time has come to put our knowledge to the test. Have you learned well the difference between oblique lines and other lines? Let’s do some exercises to find out.
Exercises with oblique lines
- Exercise 1. María is a great fan of mathematics. She loves locating objects in the world around her to find out what kind of geometric images they form. At this moment she is studying the lines. And she has a little trouble understanding the difference between oblique and parallel secant lines. Her math teacher has given her a visual example so she knows how to differentiate both types of lines. For this, she has shown him the image of a cross and some pretty scissors. She has told you that one of these images is a perpendicular secant line and the other is an oblique secant line. Can you tell us which is which and why?
- Exercise 2. Ruben loves pizza. He really likes to go to Italian restaurants to eat it. His parents have told him that there is a region in Italy that has a very similar name. It’s about Pisa. In this region is one of the seven wonders of the ancient world. The tower of Pisa. This construction seems to go against the principles of nature. Since it has been a little inclined for many centuries. And it seems that it does not expire! Could you tell us what kind of line is formed by the Tower of Pisa?
Solutions to exercises with oblique lines
If you have come this far, it means that you have already done the two exercises that we have proposed. Would you like to find out if you have found the correct solution? Let’s see it next.
- Solution to exercise number 1. María’s teacher showed her two images so that she would know how to differentiate between the types of secant lines. Some scissors and a cross. Maria had to find out which was an oblique secant line and which was parallel. Have you found out? Indeed. The scissors, with their two blades when cut, form angles that are not right. Therefore they are oblique secant lines. However, at the cross, when the two lines meet, four 90º angles are created. That is, four right angles. It is therefore a parallel secant line.
- Solution to exercise number 2. We, like Ruben, also love pizza! And the tower of Pisa seems to us a truly spectacular building. Have you found out what kind of line it forms with that highly inclined figure? Yes! It is an oblique line.