Angle Bisector

we can define  angle bisector in a line ,suppose a line is divided into equal parts means  the parts must be congruent ,there are two types of the geometry bisector there are  segment bisector and angle bisector .if the line passes through the midpoint of  a segment means we  called those kind of line as a segment bisector and the angle bisector is defined as the line will be passes through the apex of the angle and it also divides the angle  two parts  and generally   bisectors are used for divide the line into equal parts and  the line must be similar  congruent parts

Types of angle bisector:

Interior angle bisector
Exterior Angle bisector

Figure of the angle bisector:

this diagram is used for describes how  line will be split the angle into the two equal parts ,here we have to note one thing both the angles are congruent .

Angle bisector:

A line or the ray it will divide the angle into two equal parts we called as the Angle bisector.
Sometimes   line or line segment will be the angle bisector in polygon line segment is the angle bisector.
If the angle bisector divides triangle in center means we called as center of the angle bisector.

In geometry the angle bisector is divide  line into the two equal parts, both the angles are congruent


The Angle Bisector proof:

Consider the triangle, internal bisector (seen in the above diagram) divides the opposite side .So the opposite side is the ratio of the other two sides of the given triangle.

Consider the triangle has XYZ draw the line to the, it will meet the midpoint of YZ and the named the midpoint as A, so the line XA will be the internal bisector of the
Proof:

YA/AR = XY/XZ

Here the line XA will be perpendicular to the line ZB,

QS/SR = QP/PT.
YA/BZ = YX/XA XA=ZB.
In that < YXA =< XZB ----------------- (1)
Consider the corresponding angle < XBZ =And < XZB =< AXZ (we have to consider the alternate angle) ------------- (2)
From (1) and (2) we wrote the equation as shown below,
< YXA =< AXZ

So we have to tell that the point A divides YZ externally in the ratio XY/XZ, then XA is the external bisector of
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Important points:

For each and every angle there is a line, these line will intersect the angle into two halves and so that the line is called angle bisector.
Therefore angle bisectors for a triangle should be three.
The angle bisector crosses out the line so the line is called the center of the bisector.