What are the simple proofs of the Pythagorean theorem that can be mastered in the second year of jun

Draw several (at least 3) right triangles, measure the length of the 3 sides with a ruler, and see if they all agree with the Pythagorean theorem, and if they all do, then the Pythagorean theorem is proved.

In fact, it is best to learn the cosine theorem directly.

The Pythagorean theorem is an important theorem in geometry, and its formula is: a2 + b2 = c 2, where c is the hypotenuse length of the right triangle, and a and b are the two right side lengths of the right triangle. There are three ways to prove this theorem:

Construction proof: By constructing a right triangle, prove that A2 + B2 = C2.

Proof of planar Cartesian coordinate system: By studying the planar Cartesian coordinate system, it is proved that a2 + b2 = c2.

Mathematical Induction Proof: Through mathematical induction, it is proved that A2 + B2 = C2 is correct.

All three methods of proof are valid, so different people can choose different methods of proof.

The following proof is the Garfield Proof:

The area of the great square is equal to the area of the middle square plus the area of the four triangles, i.e.:

The following proof is the Garfield Proof:

The area of the great square is equal to the area of the middle square plus the area of the four triangles, i.e.:

1. The earliest record:

In China, the formula and proof of the Pythagorean theorem are recorded in the Zhou Sutra, which is said to have been discovered by Shang Gao in the Shang Dynasty, so it is also called Shang Gao's theorem; Jiang Mingzu in the Three Kingdoms period made a detailed annotation of the Pythagorean theorem in the "Jiang Mingzu Sutra".

2. Daily application:

When home decoration, workers judge whether a corner of a wall is a standard right angle. You can measure 30cm and 40cm respectively at the corner of the wall to the two walls and mark a point, and then measure whether the distance between the two points is 50cmIf the error is exceeded, the corner is not a right angle.

If you cut a small square with a side length of c on the side of a large square diagonally, you go back to the Garfield testimonial. On the other hand, if the two trapezoids in the above diagram are put together, this proves the method.

The area of the great square is equal to the area of the middle square plus the area of the four triangles, i.e.:

The three ways to prove the Pythagorean law are as follows:

Method 1] Method 2].

Method 3].

How to prove the Pythagorean theorem simply and straightforwardly.