## How is the Pythagoras theorem related to the triangle?

The Pythagorean Theorem, also known as Pythagoras’ theorem, is a fundamental relation between the three sides of a right triangle. Given a right triangle, which is a triangle in which one of the angles is 90°, the Pythagorean theorem states that the area of the square formed by the longest side of the right triangle (the hypotenuse) is equal

How to prove the Pythagorean theorem using differentials?

Proof using differentials. One can arrive at the Pythagorean theorem by studying how changes in a side produce a change in the hypotenuse and employing calculus. The triangle ABC is a right triangle, as shown in the upper part of the diagram, with BC the hypotenuse.

Which is the correct way to pronounce Pythagoras theorem?

In mathematics, the Pythagorean theorem, also known as Pythagoras’ theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

### Why was the Pythagorean theorem named after the Greek thinker?

This is known as the Pythagorean equation, named after the ancient Greek thinker Pythagoras. This relationship is useful because if two sides of a right triangle are known, the Pythagorean theorem can be used to determine the length of the third side.

How is the Pythagorean theorem based on proportionality?

This proof is based on the proportionality of the sides of two similar triangles, that is, upon the fact that the ratio of any two corresponding sides of similar triangles is the same regardless of the size of the triangles. Let ABC represent a right triangle, with the right angle located at C, as shown on the figure.