The concept of a bisector is entered still it is aware of geometry of the seventh class. The bisector is one of three main lines of a triangle which is expressed through its parties.
1. There are several definitions of a bisector. Classical definitions sound so: 1. A bisector - the beam leaving vertex of angle and halving it. 2. A triangle bisector - the piece connecting one of triangle corners to the opposite party and halving this corner. Except classical definitions, for storing, it is possible to use the mnemonic rule which sounds as follows: The bisector is a rat who runs on corners and halves a corner. DIA - any corner of SAE of a treugolnikesla is equal to EAV corner, AE piece - the bisector of a triangle of AVS leaving a corner And.
2. For formation of complete idea of a bisector it is necessary to consider its property.1. In any triangle it is possible to carry out 3 bisectors which are crossed in one point. The point of intersection of bisectors is the center of an inscribed circle in this triangle.2. The bisector of an internal corner of a triangle divides the opposite party into the pieces proportional to the adjacent parties.3. A bisector – a locus, equidistanted from sides of angle.
3. In an isosceles triangle the bisector which is carried out to the basis is at the same time a median and vyty. In that case the bisector is by means of Pythagorean theorem. where DC - a half of the party the EXPERT.
4. Formulas for, findings of a bisector of any triangle are brought out of Stewart's theorem (M. Stewart is the English mathematician). If to designate the parties of a triangle by letters a, v, s so AV = with, VS = and, the EXPERT = in where Lc is length of a bisector of b lowered on the party from AVS corner.
5. al and cl – pieces into which the bisector divides the party of b
6. triangle corners at tops And, In and With
7. N - the triangle height which is carried out from top In on the party of b.