### The perpendicular bisector of a line segment

Given a line segment AB

open the compass more than half of the distance between A and B,
and scribe arcs of the same radius centered at A and B.

Call the two points where these two arcs meet C and D. Draw the
line between C and D.

CD is the perpendicular bisector of the line segment AB. Call the
point where CD intersects AB E.

Theorem:

Given:

AC = CB = BD = AD

To prove:

- AE = EB
- CD is perpendicular to AB

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