A secant line cuts another line or a curve.
A line is a line of one dimension that is formed by an infinite number of points that follow one another in the same direction. Secant , for its part, is a concept that, in geometry, refers to the surface or line that intersects another surface or line.
A secant line , therefore, is one that cuts another line or a curve . It can be said that two lines are secant when they have a point in common (the one at which they intersect). If the lines, on the other hand, have no points in common but are still in the same plane, they are parallel lines .
Parallel lines cut by a secant
Within the set of parallel lines, we have to show that the term of parallel lines cut by a secant exists. This is frequently used within Euclidean geometry and thanks to it, a wide variety of practical problems can be solved.
When this situation occurs, where there are two parallel lines and a secant line that is responsible for "cutting" them, the "birth" of different angles occurs, depending on whose characteristics they respond to one name or another. Thus, specifically, it is usual to find the following: angles opposite the vertex, alternate internal angles, adjacent angles, alternate external angles, corresponding angles, internal collateral angles and external collateral angles.
Classification according to type
It is possible to classify secant lines in different ways. The perpendicular secant lines form, when intersected, four right angles (that is, four angles of 90º each). Oblique secant lines , unlike perpendicular lines, do not give rise to equal angles. The latter are defined by the fact that they intersect at a certain point forming equal angles two by two, two equal or similar acute angles or two equal or similar obtuse angles.
There are different types of secant lines.
If we analyze two lines based on their relationship with a curve or a circle , we can distinguish between secant lines and tangent lines . The intersecting lines, in this case, will be those that cut the curve at two points. Tangent lines only cut the curve at a single point, called the point of tangency.
Specifically, the first case is what is called, within the field of mathematics and geometry, a line secant to a curve. And therefore it refers to the line that has two intersection points on the aforementioned curve, which make up the solution set of the system, which we can determine is composed of the equations of the secant line and those of the curve.
It is important to keep in mind that all these geometric elements can be mentioned as equations through different mathematical formulas. For example: if we know two points of intersection, it is possible to calculate the equation that the secant line in question will have. To carry out the calculation you just have to resort to the appropriate formula.