Constructing Bisectors

Bisecting a Segment

A B

1) Place the needle of your compass on A. Make its width more than half-way to B, and make a half-circle.

2) Without changing the width of the compass, put the needle of your compass on B. Make a half-circle that overlaps the first one.

3) Draw a line that connects the two points of intersection of the two half-circles. That new line is both a bisector of the segment AB, and is perpendicular to AB.

Bisecting an Angle

A

B

1) Place the needle of your compass on B. Draw an arc that crosses both BA and BC.

3) Place the needle of the compass on D, and set the width to match more than half the distance to E. Make a half-circle.

5) Draw a line that connects the two points of intersection of the two half-circles. That new line is both a bisector of the angle ABC.

C

D

E2) Label the intersection of the arc and BA “D”, and the intersection of the arc and BC “E”.

4) Leave the compass width as it is. Place the needle of the compass on E, and make a half-circle overlapping the previous half-circle.