Today these skills are not required knowledge for builders. We have steel carpenter squares that have true 90* corners, as well as levels and lasers.
The carpenter squares shown here are some of the earliest made in the States. They were made in Shaftsbury and N. Bennington, VT, 1825-60. Some are on display at the Bennington Museum; all are available for study.
The 1503 woodcut at the end of this post includes a square being used for a layout. That square might not have matched the square of another builder.
Practical geometry taught how to 'prove' that an angle was 'true'. Carpenters today still make their work 'true'.
This is the end of Lesson 5.
The carpenter's assistant who masters these problems is now ready to assist in layout and framing. Maybe he (no recorded 'shes' that I know of) will go on to learn design.
For more ways to draw a square see Drawing a Square, Parts 1 and 2.
Part 1: https://www.jgrarchitect.com/2019/12/practical-geometry-drawing-square-with.html
Part 2: https://www.jgrarchitect.com/2020/01/practical-geometry-drawing-square-with.html
After-thoughts and questions: How did carpenters carry a 10' rod? Did the rod fold, or come in pieces that could be connected with pegs, perhaps leather sleeves?
I have seen one in a medieval print, part of which is shown here.
The builder on the left uses a square for layout. Below him is an axe, a saw, and a level with a triangular hole and a plumb bob.
The builder in the center holds a 10' rod. The landscape to his right is the site where he will layout a building, or perhaps land.
A 'rod' when used in land surveying is 16.5 feet long. It is also called a 'perch' or 'pole'. How did they carry that awkward length? 'Links' and 'chains' are also used in surveying, so perhaps a rod could be a length of chain.
Woodcut by Gregor Riesch, Margarita Philosophical, published in Baden,1503.