What is the bisector of the triangle?On this question in some people with language breaks down notorious saying: "This is a rat running around the corners, and dividing the angle in half."If the answer to be "humorous", then perhaps it is correct.But from a scientific point of view, the answer to this question would have sounded like this: "It's a ray starting at the top corner and dividing the latter into two equal parts."The geometry of this figure is also perceived as a segment bisector to its intersection with the opposite side of the triangle.This is not a mistake.What else is known about the bisector of the angle, in addition to its definition?
Like any locus, it has its own characteristics.The first of these - perhaps even not feature a theorem, which can be briefly expressed as follows: "If the bisector of an opposite side to divide into two parts, their ratio will fit against the sides of the big triangle".
second property, which it is: the intersection point of the bisectors of all the angles called intsentrom.
third feature: the bisector of one internal and two external angles of a triangle intersect at the center of one of the three circles inscribed in it.
fourth property bisector of a triangle that if each of them is, the latter is isosceles.
fifth sign of the same concerns of an isosceles triangle and is the main point of reference for its recognition in the drawing of bisectors, namely, an equilateral triangle at the same time it serves as a median and height.
bisector of the angle can be constructed with ruler and compass:
The sixth rule is that it is impossible to construct a triangle using the latter only when the available bisectors as impossible to build in such a way the doubling cube, the squaring of the circle and the trisection of an angle.Actually, it has all the properties of the bisector of the angle of the triangle.
If you carefully read the previous paragraph, it is possible that you are interested in one phrase."What is the trisection of an angle?"- Sure you ask.Trissektrisa bit similar to the bisector, but if the latest draw, then the angle is divided into two equal parts, and the construction of the trisection - three.Naturally, the bisector stored easier, because Trisection not taught in school.But to complete the picture and tell you about it.
Trissektrisu, as I said, you can not build a just ruler and compass, but it is possible to create with the help of rules Fujita and some curves: snail Pascal kvadratrisy, conchoid Nicomedes, conic sections, Archimedes spiral.
tasks of trisection of an angle simply solved by neusis.
In geometry, there is a theorem trissektrisah angle.It is called theorem Morley (Morley).She argues that the point of intersection are in the middle of each corner will trissektris vertices of an equilateral triangle.
small black triangle will always be inside a large equilateral.This theorem was discovered by British scientist Frank Morley in 1904.
That's how much you can learn about the separation angle: trissektrisa and bisector always require detailed explanations.But a lot has been made here have not disclosed my definitions: Snail Pascal conchoid Nicomedes, etc.Do not worry, you can write about them even more.
