Null angle

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The null angle is one that measures 0º (sexagesimal degrees) or 0 radians. It is an angle that does not exist.

In the image above, for example, we have graphed two lines in Geogebra, one that passes through points A and B and the other that passes through points A and C. The result is that both lines are superimposed on the other, forming an angle null.

We must remember that the angle is the arc formed by the crossing of two lines, rays or segments.

In this sense, a null angle is one that is identified between two coincident lines, that is, they share all their points in common. Therefore, there is no aperture that can be measured.

To know if two lines are coincident, we must check if they have the same explicit equation of the form y = mx + b. However, if we have the equations in their form 0 = Ay + Bx + C, the coefficients must be proportional, that is, limiting ourselves to the case of two lines, we would have:

A / A ’= B / B’ = C / C ’

The null angle is primarily a reference angle, that is, it serves to complement the definition of another type of angle. For example, an acute angle is one less than 90º, but greater than a null angle.

Difference between null and flat angle

It should be noted that a null angle is not the same as a flat angle, although at first glance there could be confusion between the two.

A null angle, as we already explained, is formed by two coincident lines. However, in the straight angle what we have are two rays or two segments that share only one point, but extend in opposite directions.

Null angle examples

It is difficult to think of an example of a null angle, as it is a very theoretical definition, but let's imagine that a car moves on a road (without curves) and, after this, there is another car that goes in the same direction. The trajectories of both vehicles will form a null angle.

Now, suppose that two cars start from the same point, but go in opposite directions in a straight line. In this case, the trajectories would form a straight angle and not zero.

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