Constructing Bisectors
In geometry, a bisector is a line that divides something into two congruent parts. This lesson will focus on constructing bisectors of lines and angles.
You will need:
Pencil and paper
A compass
A straightedge
Bisecting a Line Segment
We will construct a perpendicular bisector through any line segment. This means that the bisector crosses the original segment halfway at a right angle.
Step 1)
Draw any line segment with your straightedge.
Step 2)
Place your compass on one end of the segment and stretch the compass span more than halfway to the other end.
Draw an wide arc with the compass through the segment.
Step 3)
Keeping the same compass span, draw another wide arc through the segment starting from the opposite end.
Step 4)
Connect the two intersections of the two arcs with your straightedge to form the perpendicular bisector.
Constructing an Angle Bisector
We will construct an angle bisector through any angle (obtuse, right, or acute). This means that the original angle will be divided in half.
Step 1)
Draw any angle with your straightedge.
Step 2)
Place your compass at the vertex of the angle and construct an arc intersecting both legs of the angle.
Step 3)
Keeping the same compass span, construct an arc at both intersection points such that the new arcs cross inside the angle.
Step 4)
With your straightedge, connect the angle vertex with the new intersection point to form the angle bisector.
