and plugging numbers into the formula.
The following is a variety of proofs of the Pythagorean Theorem including one by Euclid. These proofs, along with manipulatives and technology, can greatly improve students' understanding of the Pythagorean Theorem.
The following is a summation of the proof by Euclid, one of the most famous mathematicians. This proof can be found in Book I of Euclid's Elements.
Proposition: In right-angled triangles the square on the hypotenuse is equal to the sum of the squares on the legs.