The origin of 勾 and 股 in The Pythagorean Theorem 勾股定理 The Chinese name for the Pythagorean Theorem is 勾股定理

Take a right angle triangle ABC

Let side AB be the shortest side.

Let AC be the second shortest side.

BC is therefore the longest side and the hypotenuse.

In Chinese the side AB is called 勾, the side AC is called 股 and the side BC is called 弦.

In English the two shorter sides are called “legs”.

Why were the two “legs” called 勾 and 股 ?

It makes sense that the hypotenuse is called 弦 as the triangle is usually drawn such that the hypotenuse is diagonal.
in ancient china, the right angle triangle is named "勾股形".

the 國語辭典 has this entry: 勾股, explained as


  我國古代稱直角三角形為「勾股形」。其直角旁的短邊稱為「勾」，長邊稱為「股」，對著直角的邊稱為「弦」。


the short side near the right angle is called "勾", the longer side near the right angle is called "股"; and the side opposite the right angle is called "弦".

people used something like "勾股", "勾股之法" to describe the equation a²+b²=c²; nowadays, a hybrid naming is used "勾股" (the ancient chinese name) + "定理" (translation of theorem).

btw, the character 句 (u+53e5) and 勾 (u+52fe) mutually borrowed in ancient time.