Question

What is the difference between a Bisector and a Perpendicular bisector?

Answer 1

Hint: Here In this question, we have to explain about the difference between a bisector and a perpendicular bisector. In Geometry, Bisector is a line that divides the line into two different or equal parts. Similarly a perpendicular bisector is a line which intersects a given line segment at a \[{90^ \circ }\] degree, and also it passes through the midpoint of the line segment.

Complete step-by-step answer:
Bisector - A Bisector is any segment, line that splits another line into two congruent (equal) parts. It is applied to both angles and line segments.

Angle bisector: A line that cuts an angle into two equal parts. In figure, the line \[JK\] bisects the angle \[\left| \!{\underline {\,
  {LJM} \,}} \right. \]. The line \[JK\] is called bisector
When, the line\[JK\] bisects the angle \[\left| \!{\underline {\,
  {LJM} \,}} \right. \], then
\[ \Rightarrow \,\left| \!{\underline {\,
  {LJK} \,}} \right. = \left| \!{\underline {\,
  {MJK} \,}} \right. \]

Perpendicular Bisector - A line or ray that cuts a line segment into two equal parts at \[{90^0}\]
In Perpendicular bisector, the bisector always crosses (cuts) the line segment (or line) at right angles at 90 degree (\[{90^0}\])
In the below figure, the line \[GF\] bisect the line \[DE\] with angle \[{90^0}\]and \[OG\] is the perpendicular bisector of \[DE\] since \[DE\] splits into two congruent segments \[DO\] and \[OE\].
 

In the triangle \[ABC\], \[ED\] bisect the line \[AC\], \[ED\] is perpendicular to \[AC\] and here triangle\[ABC\]Split into one right angle triangle and one quadrilateral

Note: Bisectors used to construct Geometrical shapes and by using perpendicular bisectors we can construct minimum one right angle triangle.
Finding the perpendicular bisector is helpful in other fields like archaeology. By carefully plotting three points on the plates circular rim, the archaeologist can reconstruct the original plates diameter from the two perpendicular bisectors of the chord of rim.