II. Erecting a perpendicular

Here is how I establish a square line at the end of a line
without using a square. I learned this when I was laying out large
steel plate. The ends of a large steel plate are rarely square, so a
square line has to be established near the end. A framing square is
not large enough to draw a line all the way across a 12’ wide plate.

You, of course, are not going to lay out any large plate using
this method. And on most of your work you will simply use a square.
But you can impress people at parties by showing them how to do
this. It is pretty cool, and if you can do this you can say that you
can do all your layout without a square.

Draw a line parallel to the side of the plate or other work.

Set your compass or divider at any convenient distance. Usually
this will be slightly less than half the distance across the plate.
Swing an arc back across the line.

Here is the arc.

Using the same setting on the compass, swing an arc to intersect
the first arc.

Draw a line of indeterminate length through the 2 points.
Indeterminate length means longer than necessary.

Still using the same setting on the compass set off another point
on the line.

Draw a line from the starting point up through the last point you
established. This line is square with the base line.

PS.
I received a post from John Lederer showing me another way to erect a
perpendicular at the end of a line.

Take a line A--B.
Place your compass center above the line, and draw a circle that intersects the
line at A and at arbitrary point D. Now draw a line from D, through the center
of the circle, till it intersects the circle again at point E. From E to A will
be a line at right angles to A-B.

Just goes to show that you are never too old to learn something new.