**GEOMETRY**

I've been tossing around terms like; erect a perpendicular, strike an arc; geometry.

Unlike what you may have thought

in Middle School; Geometry is your friend.

The most frequently used method for erecting a perpendicular

is by reference to a precise copy of a right angle - Framing/Rafter,
Speed, Combination, Try, Drywall, Miter, (the Sliding Bevel)

and the Stanley 46-101 Center Square.

The 3,4,5 right triangle and comparing diagonals? Definite force

multipliers. However, all (except the Try, Miter and Sliding Bevel squares)

involve measurement.

the “straightedge and compass constructions.”

Very useful; and often involve no measurement or calculation at all.

There's a nice compilation at mathopenref.com

with nifty animations and clear explanations.

These are the ones I used most often.

Simplest first.

Bisect a line.

Perpendicular to a line from a point

Erecting a perpendicular from a line

at a stated point

Parallel

*[Quick and dirty method for paralell** (4+ tangents - Euclid would not approve; but he might wink.)
When striking an arc you can feel the scribing end move away from and back towards you. If you know the distance from the baseline to the parallel; set your compass to that distance and strike 4-5 arcs from along the baseline; where you feel both the push and the pull. A straight line that kisses the extreme extents of all of those arcs (NOT THE POINTS WHERE THEY MAY, BY HAPPENSTANCE, INTERSECT) is parallel to the baseline at the stated distance.]*

You can also construct 60 and 30 degree angles

You can bisect an angle, very useful if you have to start from a given (and not a stated) angle

You can add or subtract angles from one another

to derive a whole assortment of useful angles.

Finding the center of a circle or an arc.

The perpendicular bisector of a chord

lies along the radius of that arc.

The point at which two or more of such radius lines (radii)

intersect is the center of that arc.

The center head on a combination square or the 46-101 Center Square both operate via the principle of the perpendicular bisector of a chord.

The points at which the two limbs of any right angle (rafter square e.g.) placed against an arc both intersect that arc, describes a diameter of that arc. The point at which two diameters intersect one another is the center of that arc.