Thanks to modern tools, drawing parallel lines or right angles is not complicated. But imagine for a moment that you live in the middle of the Fourth Egyptian Dynasty, the pharaoh of the moment wants his tomb, and all you have is rock, rope, charcoal, wood, and bronze tools. Where do you start? The YouTube channel How To Make Everything explores some of the possible solutions used by the Egyptians, and despite their apparent crudeness, they are quite effective...
They have been standing for 4,500 years, they represent the only Wonder of the Ancient World still in existence, and they still teach us things. The pyramids are not only impressive for their appearance and endurance, but also for having required a series of solutions that for decades seemed impossible to us, to the point of believing they were enabled by a superior force (you know, "aliens"). Straight and parallel lines, right angles, level bases, and the ability to repeat those conditions with precision. How did they achieve it?
Straight Lines
The YouTube channel How To Make Everything decided to explore some of those ancient techniques. For example, creating a straight line on a surface is relatively simple: Take a thin rope, soak its fibers with dye (alternatively, ash or very fine charcoal powder), place the rope in position, apply a little tension, lift the rope and "snap!", the elastic effect will make it strike the surface, leaving the line marked.
Parallel Lines
This is where we enter (a little) into speculative territory, because the second tool used is the classic marking gauge, which traces parallel lines. It consists of only three pieces: a bar, a head, and something to mark with, made of metal. Unfortunately there is very little data available about its history and origins, but it wouldn't be too far-fetched to think that the Egyptians had the equivalent of an ancestor of the marking gauge among their tools.
https://old.neoteo.com/descubren-una-misteriosa-camara-secreta-en-la-piramide-de-guiza/Right Angles
So, with straight lines and parallel lines, the next step is creating right angles. Pythagoras is not an option (he was born 2,000 years after the pyramids), and the simplest thing would be to make a square with errors, measure in both directions and take the intermediate value between both twisted lines. Another possibility is to use overlapping circles, with a parallel line passing through the center of both. The points where they intersect should form a line that, when passing over the parallel line, gives us four right angles.
The Perfect Square and Plumb Line
The last piece of the puzzle is the creation of a perfect square (or at least, with an angle as close as possible to 90 degrees), and the connection of a plumb line (although it is made of bronze) to obtain verticality. The unit of measurement chosen for the creation of a hypothetical stone block is none other than the royal Egyptian cubit (equivalent to about 0.52 meters), with each block measuring 2.5 by 2.5 by 1 cubit. When comparing the results with modern tools, it is evident that their measurements have errors... but they got closer than expected. With better construction of each tool (mainly the square), those differences would be even smaller. In short, no aliens. The Egyptians had brains, and they probably knew how to use them.
https://old.neoteo.com/ramses-ii-la-momia-que-obtuvo-pasaporte/