you need
  • - book;
  • - pencil;
  • - line.
prove the theorem it is impossible without the knowledge of its components and their properties.It is important to note that the bisector of the angle, according to the conventional concept, is a ray emanating from the vertex of the angle and divides it into two equal angles.This bisector is considered a special locus of the points in the angle that are equidistant from its sides.According to the nominated theorem bisector is also a segment that goes from the corner and crosses to the opposite side of the triangle.This statement and should prove.
Check out the concept of the segment.The geometry of the straight line is bounded by two or more points.Given that a point in the object is abstract geometry without any characteristics, it can be said that the length - the dist
ance between two points, e.g., A and B. The points constraining segment called its ends, and the distance between them - of its length.
proceed to the proof of the theorem.Formulate a detailed condition.To do this, you can consider a triangle ABC bisector BK, coming out of the corner of V. Prove that the BK is a segment.With the swipe across the top of the line SM, which will be held parallel to the bisector of the VC to the intersection with the side AB at M (for this side of the triangle should be continued).Since VC is a bisector of the angle ABC, then the angles ABK and the PIC are equal.Also, the angles will be equal to AVC and Navy because it corresponding angles of two parallel lines.The following fact is the equality of the angles KBC and SCM: the angles lying crosswise at parallel lines.Thus, the angle equal to the angle BCM Navy, the Navy and the triangle is isosceles, so BC = BM.Guided by the theorem of parallel lines that cross the side of the corner, you'll get equality AK / COP = AB / BM = AB / BC.Thus, the internal bisector of the angle of a triangle divides the opposite side in the proportion to its adjacent side parts and is a segment, as required.