Constructing a Perpendicular from the Endpoint of a Segment

Given a segment AB, I need to construct a perpendicular line starting from one of its endpoints.

First, I set my compass to any convenient width and place its center at the endpoint where I want to construct the perpendicular.

For example, I position the compass at point A and draw an arc.

This arc intersects segment AB at a point, which I label as C.

Keeping the compass at the same width, I now place its center at C and draw a second arc.

The two arcs intersect at a new point, which I call D.

Without adjusting the compass width, I now center it at D and draw another arc.

This arc intersects the first one at a new point, which I name E.

Still keeping the compass at the same width, I now place its center at E and mark point F at its intersection with the previous arc.

Finally, I draw a straight line through points A and F.

This line is perpendicular to segment AB and originates from its endpoint.

Therefore, segment AF is perpendicular to the endpoint of segment AB.

And that’s it!