How can I construct a bisector of an angle with a circulation and a ruler ℹ️ Definition, order of geometric construction and division into equal parts, proof

Rough-boiled triangle

Construction process

Bisectrix (Lat. Bisectio) is a geometric point of points inside the angle (acute, straight or stupid), which are equally removed from both sides.

To build it, you need to prepare various school supplies and perform a few simple actions.

Preparatory stage

To quickly find the triangle bisector with a circulation, you need to spend thorough preparation. It is to find school supplies to be used when constructing.

Necessary subjects:


  • simple pencil;
  • line;
  • eraser;
  • compass;
  • paper.


Draw a beam separating in half an angle, you can use the vehicle. However, if this school supplier is not available, an ordinary circulation will be able to replace it.

Fast way:


  1. On the sheet of paper they paint 2 intersecting lines.
  2. To build a bisector of this angle, in its vertex they put the feet of the circulation and the circumference of the arbitrary radius.
  3. Note the points of the intersection of the side of the corner with a circle.
  4. They alternately put a circulation and, without changing the radius, draw 2 arcs.
  5. Find and mark their intersection.
  6. Erase arc by the eraser so that they do not interfere with further work.
  7. Using the ruler and simple pencil, the desired segment connects the top of the angle with the point of intersection of the arc.

With the help of a circula, you can easily find the triangle bisector (all). To do this, you will need a standard set of school supplies and the presence of basic knowledge of geometry.


  1. In any known way, the circle in the triangle fit into the triangle.
  2. With the help of a pencil and line from its center conduct lines to each vertex.
  3. The resulting segments will become part of the desired beam.

Alternative option

If the student has no circulation, then draw the ray, separating the angle in half, can be without this school supplies. It will take a ruler, pencil and transport.

What is Biseektrissa

The correct sequence of actions:

Work with Tsyrkule

  1. The zero value on the scale is applied to the top.
  2. Combine the transport line with one of the rays and determine the magnitude of the angle.
  3. The resulting value is divided by half.
  4. Then the transportation is re-applied and the magnitude obtained as a result of the calculations is deposited.
  5. Through this point and the vertex is made of a segment that will be the desired beam.

Useful advice

In some cases, it is not necessary to use the vehicle and the circulation. This is only possible when it is necessary to determine the location of the bisector in the triangle.

Useful recommendations:

  1. Bisectrix always separates the opposing side of the triangle in relation to equal to the proportion of 2 other sides of the geometric shape.
  2. In an equilibried triangle, bisector always intersect at right angles.
  3. If the triangle is equilateral, all the bisector will be parallel to the opposite sides. At the same time, the length of the formed segments will be the same.

To construct a bisector of an angle with the help of a circulation, even a two-way. To do this, he will need a minimum of time, knowledge and effort. After examining in detail the procedure, each student can easily divide any angle in half and explain this process to classmates.

How to build angle bisector with a circulation Bissectrice Angle They call the beam, which comes out of the top of the angle and divides the specified angle by 2 angle, equal to each other. Rather how to construct bisectris of any angle, having a ruler and circula.  

  1. A corner is set to the vertex at the point A, the bisector of which needs to be built. This angle comes out of the vertex A.

We put the circus to the point A and carry out a circle of any radius R. The specified angle will cross with a distinguished circle at two points. Let's call them in and S.

  1. Blacks are still two circumference of the same radius with centers at points B and C. When crossing these two drawn circles, we obtain a point that let's call D.

  1. Using a ruler from the point and through the d point D we carry out a ray. The resulting beam and will be a bisector of a given angle A.

There are several rules that can help you find a bisectaris. For example: - Bissektris divides the opposite side of the triangle in such a respect, which is equal to the ratio of the other sides; - two corner bisector at the base of an anose-free triangle are equal; - all three bisector of any triangle will intersect in the center Inserted into this triangle of the circle. Also, you can construct a bisector with the help of the transporter. For example, if you need to build an angle of 78 degrees, you need to attach the vehicle to one of the sides of this angle, mark the point near the mark 78/2 = 39 degrees and spend Ray from the vertex of a given angle through the resulting point. This will be the bisector an angle of 78 degrees.

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