# Bisecting a Line Segment with a Ruler Given a Parallel Line

Bisecting a Line Segment with a Ruler Given a Parallel Line

Suppose the segment lies on the line and that a line is parallel to .

AB

a

b

a

This Demonstration shows how to bisect using only a ruler.

AB

1. Choose a point not on or .

P

a

b

2. Let the segments and intersect at points and , respectively.

AP

BP

b

D

C

3. Let the segments and intersect at point .

AC

BD

E

4. Then the line intersects at the midpoint of .

PE

a

M

AB