The most famous relation in geometry is the relation between the sides and the hypotenuse of a right triangle.

几何中最著名关系是直角三角形和斜之间关系。

Take four identical right triangles with side lengths a and b and hypotenuse length c.

取等直角三角形，两分别长 a 和 b，斜长 c。

Root 2 simply is the hypotenuse of a right triangle

而 √2 只是两长 1 直角三角形之斜。

After the hymn, the teacher taught students the hypotenuse.

赞美诗后，老师教学生直角三角形斜。

When you draw a vector, it's a lot like the HYPOTENUSE of a right angle triangle.

当你画一箭头时，它很像 直角三角形斜。

That states that the squares of the sides of a right triangle add up to the square of its hypotenuse.

这表明直角三角形各平方加起来等于其斜平方。

They all came up with elegant proofs for the famous Pythagorean theorem; the rule that says for a right triangle, the square of one side plus the square of the other side is equal to the square of the hypotenuse.

他们都对毕达哥拉斯定理（勾股定理）做出了精彩证明；这定理是说，对于一直角三角形，一平方加上另一平方等于斜平方。

They all came up with elegant proofs for the famous Pythagorean theorem, the rule that says for a right triangle, the square of one side plus the square of the other side is equal to the square of the hypotenuse.

他们都著名毕达哥拉斯定理提出了优雅证明，这条规则说对于直角三角形，一侧平方加上另一侧平方等于斜平方。