Two lines in a Cartesian plane can be coincident, parallel, perpendicular, or intersecting. Thus, two lines are coincident when they overlap, since they fully coincide as all their points are in common. Two lines are parallel when they do not have points in common, that is, no matter how long they last, they will never be cut. Two lines are perpendicular when they have only one point in common and, therefore, they intersect at that point of contact.
On the other hand, the perpendicular lines that meet at the point of contact form four right angles (90 degree angles). Of the angles represented in two perpendicular lines, it is sufficient to indicate one of them, which is done by means of a small square and a point inside it (in this way it is indicated that there is a right angle or 90 degree angle and that the other three angles also have the same measure). Two lines are intersecting when they intersect, that is, they have only one point in common, but right angles are no longer formed at the point of contact.
Distinction between perpendicular line and intersecting line
As can be seen, the perpendicular lines are similar to the intersecting lines, but with a difference in relation to the angles (in the intersecting lines there is an acute angle and another that is obtuse). This distinction is important, since the term perpendicular is sometimes used inappropriately.
We speak of perpendicular lines and this implies that there is perpendicularity, a concept of Euclidean geometry or plane trigonometry that allows us to understand the formation of some figures. For example, if we think of a right triangle, we are dealing with a figure with a right angle because two perpendicular lines appear in it, the same as the square or the rectangle.
Perpendicularity is a mainly geometric concept and is applicable to all kinds of disciplines and realities. In this way, in the professional field of drawing, architecture or engineering, perpendicular lines are drawn to make the plan of a house, an urban layout, a road or a map of railway lines.
In everyday life, exactly the same happens when we make a sketch or consult a map of a city. In short, perpendicularity exists to the extent that we are able to explain space in its geometric dimension.
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