Euclid's Proof of the Pythagorean Theorem

This excerpt proves the Pythagoras' Theorem using Euclid's proof.


Prove the the Pythagoras' Theorem, using Euclid's proof.


by AskAI
Pythagoras' Theorem states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

Euclid's proof is as follows:

Let ABC be a right angled triangle, with the right angle at C.

Draw the square on each side, and label the length of each side as shown.

Now we have four congruent triangles:

We can see that:

AC = A'C'

BC = B'C'

AB = A'B'


AC^2 = (A'C')^2

BC^2 = (B'C')^2

AB^2 = (A'B')^2

Now we can see that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.

A.I. Evaluation of the Solution

The candidate's solution is complete and solves the problem. The approach is clear and easy to follow.

Evaluated at: 2022-11-11 03:30:30