Thursday, May 26, 2022

Plane Geometry Theorems vs Axioms Sky Academy

hi this is soon and i'm the principal and director of sky academy and um in the last episode what we did was looked at some looked at plane geometry and done some introductory definitions on plane geometry .

Point interval ray line angle okay so now in this episode i actually want to look at a couple more definitions or two more definitions in particular theorem versus axiom now you may or may not have heard those words and you don't really need to know them but let me just explain what they are so that this will .

Help you when you're doing geometrical proofs or communicating geometrical proofs okay so geometrical proofs are kind of like um like writing an essay in mathematical language where you kind of build on an argument or build on a statement of facts .

And you kind of work your way towards proving something is is something else or something is true okay which is what the question might be asking okay and to do that you need to rely on things called theorems or axioms all right now let me just kind of go .

Through what a theorem or axiom is a theorem is something that you can prove to be true okay so what's an example of a theorem pythagoras's theorem is something that you know remember pythagoras's theorem says that in a right angle triangle .

The square of the hypotenuse is equal to the sum of the square of the the two shorter sides that's something that we can prove all right because it's something that we can prove to be true we call that a theorem okay and the essay that we use to communicate its truth .

Is called um the proof all right so a theorem is a statement that requires proof or can be proved to verify the truth of it this differs with the word axiom which you may or may not have heard okay but an axiom is just a mathematical statement okay um and in the strictest sense of .

The word an axiom is something that you can't prove it to be true okay but um you kind of assume it to be true you kind of have to assume it to be true in order to build um on mathematical rules so it's kind of like a mathematical rule that is assumed to .

Be true so it's a statement that is assumed to be true that allows further truth to be proved or to be discovered okay so that's an axiom and i'll give you an example of an axiom i suppose an axiom a good example of an axiom is the one that we have here that an interval or a line is the .

Shortest distance between two points is it really the shortest distance between two points now i understand that in in physics and in the um in science that's not necessarily the case all right so the shortest distance between two points isn't necessarily a straight line .

In in physics or science okay it's something else called i don't know it's but um but we won't go there right but so they're the two things that we need to know and in plain geometry what we will be doing is we will be looking at a whole lot of axioms .

And theorems that we will be using to help us prove geometrical type problems okay so an example of this might be something that you might know from junior school um supplementary angle is equal to 180 degrees a straight angle equals to 180 degrees .

Um the angle sum of a triangle is 180 degrees corresponding angles on parallel lines are equal right so these are what we call either theorems or axioms and but we'll be using them and you don't need to know these two words but .

We'll be using them using these theorems and axioms to help us solve um geometrical type problems okay so we need to be aware of of theorems and axioms and when i refer to them that's what i basically mean okay so that's all i wanted to do for this episode .

In the next episode we will launch straight into it and start looking at some axioms together all right so thank you very much for watching you

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