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Bisector

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We know by the name of the bisector of a triangle the segment that, dividing one of its three angles into two equal parts , ends on the corresponding opposite side . There are three bisectors ( Ba, Bb, and Bc ), depending on the angle at which you start.

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What is the bisector?

The bisector of an angle is the ray that has its origin at the vertex of the angle dividing it into two angles that have equal measure. It is the place geometric points the plane of rays of an angle .

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  • Definition
  • features
  • Properties
  • How the bisector is drawn
  • Angle bisector
  • Bisector of a triangle
  • Bisector of a segment
  • Perpendicular bisector
  • Examples

Definition

The bisector is a term that is used in the area of geometry and as a definition we can say that it is a line that, when passing through an angle, is able to divide it into two totally equal parts. If we speak from the point of view of geometry, the points that have a bisector are parallel , this means that they have the same distance in the rays of an angle.

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It is important to note that the group of points that are placed on one side of the fixed point that the line has is known by the name of geometric place , it has an origin point and like all lines it expands to infinity , or is, it has no end. In the same way, the point of the bisector will have the same distance as the two lines of the angle , due to their correlation. When two lines are connected they give rise to four angles , and each of these angles has the function of determining a bisector .

features

The main characteristics of a bisector are the following:

  • All the points that have a bisector are parallel and for this reason have an identical distance to those of the ray at an angle.

Properties

Like many geometric figures, the bisector also has properties that differentiate it from others, among them we can mention that:

  • The points of the bisector are considered equidistant from the two sides of the angle.
  • Two lines, when they intersect, determine four angles consecutively and their bisectors, passing through the point of intersection, form four right angles that are all consecutive.
  • The bisector of an angle, with each of the sides has the possibility of forming two angles with common and equal sides, each of them is half of the original.

How the bisector is drawn

In order to draw or build a bisector we must follow the following steps:

  • An angle must be drawn .
  • Nominate with the letters A, O and B , the angles.
  • Using a compass we center at vertex 0 .
  • We draw an arc of any radius that is the one that will cut sides a and b.
  • With the compass , we center on the points P and Q and then draw two arcs with the same radius and then cut at point A .
  • Using a ruler, we draw a line that joins vertex 0 with point A, and in this way we can obtain the bisector of the angle .

Angle bisector

The bisector of an angle is the line that divides the angle into two equal parts when it passes through its vertex . In order to draw the bisector of an angle we must follow the following steps:

  • Plot a circle of any amplitude at the center of the vertex of the angle.
  • From the points where the circumference cut with the sides of the angle is made, two circles that have the same radius must be drawn .
  • The line that passes through the vertex of the angle and one of the intersection points of the circumferences is known as the bisector of the angle .

Bisector of a triangle

We can define the bisector of a triangle as the segment that, dividing one of its three angles into two equal parts , ends on the opposite side of the triangle. It is important to mention that there are three bisectors which are: Ba, Bb and Bc , depending on the angle at which it starts. The length of the bisectors are calculated with the formula :

a = (2 / (b + c)) √ (b c s (sa))

b = (2 / (a ​​+ c)) √ (a c s (sb))

c = (2 / (a ​​+ b)) √ (a bs (sc))

Where a, b and c are the three sides of the triangle and s the semiperimeter:

s = (a + b + c) / 2

The three bisectors that a triangle has converge at a point known as the incenter (I), which is always an interior point that exists in any triangle .

Bisector of a segment

In geometry, it is known to segment the fragment of line is included between two points , which points are called ends or end . The bisector or bisector of a segment is then a line or a line segment that passes through the midpoint of a certain segment.

Perpendicular bisector

The perpendicular bisector is a different way of calling the bisector , that is, the line that is perpendicular to a segment and that passes through its midpoint . In order to make a difference from the bisector, we then call this bisector angular , although it can also be known as a perpendicular bisector . A bisector can be a perpendicular bisector only if the bisector is perpendicular to the segment .

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