why a^2 + b^2= c^2we are learning about the pythagorean theorum next week i'm not really in high school
The pythagorean theorem has many proofs, for your level we can opt of the simple geometric/algebraic proof.
If we construct a large square by joining 4 right triangles as follow in the picture, we will find the area of that square using two different strategies.
Area of each triangle is `1/2ba`
We have 4 of them so area of all 4 is `4*(1/2ab)=2ab`
The small interior square has (b-a) as measure of its side, so its area is `(b-a)^2=a^2-2ab+b^2`
Hence total area is `2ab+a^2-2ab+b^2=a^2+b^2`
Since the larger square has side c then its area is `c*c=c^2`
Both strategies give the area of the same square, thus
Hope this was helpful. There is a similar proof if we rearrange the triangles similar to the 3rd attached figure, I will attach a link where you can find that proof.
Good luck in high school.