The site www.cheops-pyramide.ch is about how Egyptians were able to achieve an incredible precision when measuring with simple techniques. I'm going to summarize it.
1. Right angles in the corner
The base of the Cheops pyramid forms a perfect square - the deviation from the 90° angle is a maximum of one minute, which is very precise when you consider the Cheops pyramid's side length of 440 Egyptian Cubit or 230.33 meter.
By stretching a cord between two pegs stuck in the ground, a long straight line was marked out. Then to each peg an equal length of string was tied, more than half as long as the line drawn. By keeping the strings stretched tight and moving the ends around, the Egyptians could draw parts of two perfect circles. These arcs cross each other at two points. By drawing a straight line between these two points the original line is bisected at a right angle and the line is cut into two equal parts.
The second method is more astonishing. Although ancient Egyptians did not know the theory behind the Pythagorean Theorem (a² + b² = c²), they did use it unknowingly. They used a so-called primitive Pythagorean triple 3-4-5 (3² + 4² = 5²). Take a long rope, divide it with knots into 12 parts from the exact same length. When you now lay out your rope as a triangle and use 3 parts, 4 parts and 5 parts as side lengths, you get a perfect right angle between your 3 parts and 4 parts side
If needed, they extended the range or size of their triangle by using multiple rods of the same length. Remember, they were handling with 230 meters as one side length
2. Control of the inclination angle with the seked
The Egyptians didn't knew the division of the angle in 360°. From the Rhind Papyrus we know that the Egyptians calculated with a so-called "seked". The return (horizontal displacement) of a wall is measured. Or in other words: How many palms (7.48cm) and fingers (1.87cm) is the upper edge of the wall set back to the lower edge, namely at a height of an Egyptian Cubit (52.4 cm).
For the Cheops pyramid, the documented Seked was 22 fingers or 5 palms and 1 finger. This results in an inclination angle of 51.84° and only a very tiny difference to the official measurement which is 51.84444°.
3. Leveling the pyramid base
The Cheops pyramid's base area, a square of 230m x 230m (= 52900 m²) has a height difference of only 2.1 cm. This is a remarkable achievement.
The ancient Egyptians knew the square level, which is a right-angled isosceles triangle made from wood. This tool is made in the shape of the letter "A" and looks like a triangle ruler. A plumb-line is suspended from the top of the connected corners. If the plumb bob coincides with a mark in the middle of the crossbeam, the surface area on which the two legs stand is level. By placing this triangle on stone, these could be easily leveled.
Field tests have shown that this method could be used to measure a distance of 45 meter up to a centimeter. Longer distances like our 230 meter do not go, because then the human eye sees too little detail. So far we have three discoveries of such wood triangles, approximately from the grave of Sennedjem at Deir el-Medineh.
4. Aligning the three main pyramids
Unfortunately, the linked source does not go into detail on how the ancient Egyptians did it. But as shown in the picture, all three pyramids are aligned at their square diagonal.
5. Orientation to the north
The pyramids are nearly aligned to true north (deviation is only 2.46°).
A small but precisely worked pyramidion (made from wood or stone) is placed as close as possible to a north-south position on the flattened ground where the pyramid will be built. Then two lines are drawn, taking the edges of the small pyramidion and lengthening them on the side which lies in the shadow. During a day a surveyor notes down, where exactly the tip of the pyramid shadow cuts through those two lines. The pyramidion is precisely aligned north to south, when both lines are cut at the same distance to the corner of the pyramidion. To achieve this, the pyramidion is moved slightly over a period of days, until both segments are exactly the same length.
There is some historical evidence that ancient Egyptians know a rope roll (that's not a pulley or pulley block). With the help of the rope roll it is possible to haul a 2.5 tons stone block including sledge up the 52° incline of the flank of the pyramid.
This technique can be compared to slinging a rope attached to something heavy up over a branch of a tree and then pulling the heavy object up by grabbing the rope and walking a short distance away from the tree. If you walk down a steep incline you need even less force than on level ground.
7. Waterproof joining of stone blocks
The outside surface stones are cut within 0.01 (1/100th) inch of perfectly straight and at nearly perfect right angles for all six sides. And they were placed together with an intentional gap between them.
That 0.02-inch gap was designed to allow space for glue to seal and hold the stones together. A white cement that connected the casing stones and made them watertight is still intact and stronger than the blocks that it joins
Land surveying and the Orion constellation
After answering some of your questions, here's a point for further answers: How did the ancient Egyptians measure their land and use the whole Nile Delta to depict the Orion constellation onto it? We are talking about a distance of 8 kilometers (Pyramid of Djedefre to Gizeh) or 4 kilometers (two unfinished pyramids at Zawiyet el-Aryan to Gizeh)
All pyramids are tied together. The three main pyramids are standing for the Orion belt. And two of the four outer stars exists as smaller (not so famous) pyramids. Only 2 stars are not represented. But they found plans for one more pyramid which should be build at the right position.
- Pyramids of Zawiyet el-Aryan - Betelgeuse
- Cheops pyramid - Al Nitak (left belt-star)
- Chephren pyramid - Al Nilam (middle belt star)
- Menkaure pyramid - Al Mintaka (right belt-star)
- Djedefre pyramid in Abu Roash - Rigel