Foundations of geometry

Foundations of geometry is like a game where we try to figure out how things exist in the world. The game has rules, which are called axioms, that we have to follow to play the game correctly. Each axiom makes a claim that we have to accept as true to keep playing the game.

Once we have accepted the axioms, we can start building things like shapes and figures by drawing lines and angles. These things are called objects in the game. We use terms like congruent, perpendicular, and parallel to describe these objects.

To make sure that the game is fair, we also have some proof techniques. We use these techniques to show that one thing is true based on what we have already claimed to be true. The most important proof technique is called deductive reasoning. It means that we can use the axioms and things we have already proven to prove something new.

The foundations of geometry game is very important because it helps us understand how things in the world work. We use geometry all the time, like when we measure things or design buildings. Without geometry, we wouldn't be able to do these things.