Angle bisector


The bisector of an angle is that ray that, starting from the respective vertex, divides an angle into two equal parts.

That is, the bisector is the line that divides the angle into two portions of identical measure. That is, in the lower image, if α is 70º, it will be divided into two 35º angles.

At this point, we must first remember that the definition of angle is the arc that is formed from the union of two lines, rays, or segments.

Likewise, we point out that a ray, like the bisector, is defined as the portion of the line that has a point of origin and extends to infinity. That is, unlike a segment, it does not have two, but only one end.

How to draw a bisector

To draw a bisector, we first draw a circle of any amplitude, taking as the center the vertex from which the angle is formed.

Next, we will observe that the rays that form the angle intersect the circumference at two points. Taking each of them as the center, two circles with the same radius are drawn.

Then, the ray that crosses the intersection between the last two circles drawn will be the bisector of the angle.

It should be noted that when drawing the bisectors of the three angles of the triangle, they will intersect at the incenter of the figure, which is the center of the inscribed circle (inside) of the triangle.

As we see in the figure below, I is the incenter of triangle ABC. It should be noted that the equidistant incenter of the sides of the triangle, that is, observing the image, the ID segment is equal to the IE segment and, in turn, equal to the IF segment.

It is worth mentioning that in our article on the bisector of a triangle we define it as a straight line, although its essential characteristic is the same and it divides the internal angle of the figure into two equal parts.

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