The correct answer is C. prove.
Pythagoras was a Greek philosopher and mathematician who lived in the 6th century BC. He is best known for his Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Pythagoras is also credited with being the first to prove the universal validity of geometrical theorems. This means that he showed that geometrical theorems are true for all triangles, regardless of their size or shape.
The other options are incorrect. Option A, give, is incorrect because Pythagoras did not simply give the Pythagorean theorem. He proved it. Option B, both, is incorrect because Pythagoras did not both give and prove the Pythagorean theorem. He only proved it. Option D, none of the above, is incorrect because Pythagoras did prove the universal validity of geometrical theorems.