Bisectors

When a point moves in one direction and also in its reverse direction, the geometrical figure thus obtained is a line. In other words, any geometrical figure which is  straight with  no volume and which extends in both directions infinitely is called a straight line. A line has no end points.

 

 

Angle bisector theorem:

In geometry bisection is nothing but the division of something in to two equal and congruent parts.

Consider a triangle ABC; let the angle bisector bisect the line BC at the point D, so that the line will be divided in to BD and DC. The ration of BD to DC will be equal to the ratio of the line AB to the line AC.

/files/tvcs/trianglebisector.gif

 

Part of stright line with definite end points is called a line segment. Bisect means to cut or to divide into two equal parts. A line that divides another line segment into two equal parts or a line which divides an angle into two equal angles is called a Bisecting line. There are two types of bisectors which are often referred types of bisectors. They are (a)The line segment bisector  (b) the angle bisector.

 

Types of bisectors:

 

There are two types of bisectors in triangles. They are,

1)    Angle bisector

2)    Line segment bisector

Angle bisector:

/files/tvcs/bisectangle.gif

Angle bisector is one of the types of bisectors, it is divides the angle in to two angles of equal measure. It has only one bisector. Interior bisector of an angle is the line which divides the angle in to two equal angles along same side as angles.

/files/tvcs/anglebisect.gif

One of the the types of bisectors, define the exterior bisector  of an angle is the line which divides the angle in to two equal angles on opposite side as angles. By keeping vertex as the center one has to draw a circle. The circle cuts the angle at two points. Using that point as centre draw two circles of same size. The intersection of the circles determines a line that is the angle bisector.

 

Line segment bisector:

 

Another one type of bisectors is line segment bisector. It is passes through the midpoint of the line segment. Perpendicular bisector has the property that it meets the segment at right angles. The perpendicular bisector is equidistant from the endpoints of the segment.

/files/tvcs/linesegbisect.gif

The bisector can be drawn by following method. The circle is drawn in the perpendicular bisector it will cut at two points. By keeping that as the center point we have to draw two circles which cut each other at some point. By keeping the center as reference if we draw a line perpendicular to it then we will get the types of bisectors are called line segment bisector.