# why a^2 + b^2= c^2we are learning about the pythagorean theorum next week i'm not really in high school

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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.

1st strategy:

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`

2nd strategy:

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

`c^2=a^2+b^2`

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.

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