Much used compass and straightedge constructions

Question

I am a editor of wikipedia and would like to know which compass and straightedge constructions deserve a place in the list https://en.wikipedia.org/wiki/Compass-and-straightedge_construction#Much_used_compass-and-straightedge_constructions .

This list is a bit a list of constructions you should master and could be refered to when making instructions for more complex constructions

Off course all constructions can be reduced to a (long) list of basic constructions. But rewriting a complex constructions to a list of basic constructions is very cumbersome and repetitive.

The constructions in this list should not be for final constructions (like https://en.wikipedia.org/wiki/Pentagon#Construction_of_a_regular_pentagon ) but for naming the repetitive building blocks that help to shorten the instruction list for complex constructions

Off course each answer will be a bit subjective , but many answers will make the list more objective (I hope)

Answer 1

In their Geometričeskie postrojenija na ploskosti (1957, in Russian, “Geometric constructions in the plane,” p. 29), Argunov and Balk write:

A number of the simplest geometric construction problems serve particularly often as components in the solutions of more complex problems. Problems of this kind are generally examined at the beginning of the school geometry curriculum. We will call them elementary geometric construction problems. Of course, the list of elementary problems is a matter of convention. The following problems are usually classified as elementary:

1. The bisection of a segment.
2. The bisection of an angle.
3. The construction on a given line of a segment equal to a given one.
4. The construction of an angle equal to a given one.
5. The construction of a line passing through a given point parallel to a given line.
6. The construction of a line passing through a given point and perpendicular to a given line.
7. The division of a segment in a given ratio.
8. The construction of a triangle with three given sides.
9. The construction of a triangle with a given side and two given adjacent angles.
10. The construction of a triangle with two given sides and a given angle between them.
11. The construction of a line passing through a given point and tangent to a given circle.
12. The construction of a right triangle from its hypotenuse and one leg.