# 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.