This lesson explains how to construct angle bisector and perpendicular bisector.
An angle has only one bisector. Each point of an angle bisector is equidistant from the sides of the angle. In case of ABC,
BD is the bisector as it splits the angle into two angles of equal measure mABD
= mDBC.
The interior bisector of an angle is the line or line segment that divides it into two equal angles on the same side as the angle. The exterior bisector of an angle is the line or line segment that divides it into two equal angles on the opposite side as the angle.
Steps to Construct Angle Bisector:
• Draw an arc that is centered at the vertex of the angle (say B).
This arc can of
any radius. It must intersect both sides of the angle (say AB
and CB). Give the intersection points some name (say R and S)
• Now draw two more arcs. First arc should centered on one of the two points R
or S and the second arc should centered on the other point. The radius for both the
arcs must be same and the arcs must intersect in at least one point. Let the intersection
point be X.
• Draw a line from vertex B passing through X. Mark the endpoint of this line as D. So BD is the angle bisector.
(More text below video...)
(Continued from above)
A perpendicular bisector CD of a line segment AB is a line segment perpendicular
to AB and passing through the midpoint.
Steps to construct Perpendicular Bisector:
• Place the compass on one end of the line segment(say at A of
line segment AB).
• Set the compass width to a approximately two thirds of the length of the line.
• Then draw arcs on both the sides of the line.
• Now with same compass width, place the compass point on the the other end (say
B).
Draw arcs on both sides of the line such that the arcs cross the first two. Name
the intersecting points(say C and D).
• Draw a line passing through both the intersecting points of the arcs. CD
is the perpendicular bisector of AB.
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