What is the difference between the cosine theorem and the Pythagorean theorem?

The cosine theorem is derived from the Pythagorean theorem.

The Pythagorean theorem only applies to right triangles, and the cosine theorem applies to any triangle.

The cosine theorem can be proved by the Pythagorean theorem of a right triangle; According to the cosine theorem, when the sum of the squares of the two sides of a triangle is equal to the square of the length of the third side, the corresponding internal angle of the third side must be a right angle, that is, the triangle must be a right triangle.

If two triangles have two sets of corresponding sides and the angles between the two sets of edges are equal, then the two triangles are congruent. The area of the triangle is half the area of the parallelogram at the same base and height. The area of any square is equal to the product of its two sides.

The area of any one rectangle is equal to the product of the length of its two sides.

The Pythagorean theorem states that the sum of the squares of the sides of two right-angled sides (i.e., "hooks" and "strands") of a right triangle is equal to the square of the sides of the hypotenuse (i.e., "strings"). That is, the Pythagorean theorem is an application of the cosine theorem to right triangles.

The perturbation relationship between the Pythagorean theorem and the cosine theorem is demonstrated as follows:

1. The Pythagorean theorem is a basic geometric theorem, which states that the sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse.

2. The cosine theorem is that for any triangle, the square of either side is equal to the sum of the squares of the other two sides minus the product of two times the cosine at the angle between the two sides and them.

3. The cosine theorem is a mathematical theorem that describes the relationship between the length of three sides and the cosine value of an angle in a triangle.

4. Therefore, the relationship is that the cosine theorem is a generalization of the Pythagorean theorem in the case of a general triangle, and the Pythagorean theorem is a special case of the cosine theorem.

Pythagorean theorem: In any right-angled triangle, the sum of the squares of the two right-angled sides must be equal to the squares of the hypotenuses. This theorem is also known as the "Shang Gao Theorem" in China and the "Pythagorean Theorem" in foreign countries.

The Pythagorean theorem (also known as Shang Gao's theorem, Pythagorean theorem) is a basic geometric theorem that was discovered by Shang Gao as early as the Shang Dynasty in China. It is said that after Pythagoras discovered this decision, he immediately beheaded a hundred oxen to celebrate, so it is also called the "Hundred Oxen Theorem".

The Pythagorean theorem states:

The sum of the squares of the two right-angled sides (i.e., "hooks", "strands") of a right triangle is equal to the square of the sides of the hypotenuse (i.e., "chord").

That is, let the two right-angled sides of a right-angled triangle be a and b, and the hypotenuse side is c, then.

a2 + b2 = c2

The Pythagorean theorem has now found about 400 ways to prove it, making it one of the most provable theorems among mathematical theorems.

Pythagorean array. A positive integer array satisfying the Pythagorean theorem equation a2 + b2 = c2 (a,b,c). For example, (3,4,5) is a set of Pythagorean arrays.

Since there are 3 unknowns in the equation, there are countless groups of Pythagorean arrays.

GeneralizationIf the hypotenuse of a right-angled triangle is regarded as a vector on a two-dimensional plane, and the two hypotenuses are regarded as projections on the coordinate axes of the plane Cartesian coordinate system, the significance of the Pythagorean theorem can be examined from another perspective. That is, the square of the length of a vector is equal to the sum of the squares of the length of the projection on a set of orthogonal bases in the space in which it is located.

It is the Pythagorean theorem, which is the Pythagorean theorem.

In an RT triangle, the sum of the squares of the two right-angled sides is equal to the square of the hypotenuses.

Pythagorean theorem.

It's the Pythagorean theorem:

In our country, put right triangles.

The sum of squares of the two right-angled edges is equal to the hypotenuse.

This property of the square is called the Pythagorean theorem or the Pythagorean theorem.

In the nine chapters of arithmetic, there is a saying that hook 3 strands, 4 strings, 5 strings).

The ancient Egyptians used knots to make the RT triangle theory, also known as the Pythagorean theorem.

or Pythagoras

theorem）。

Theorem: If the two right-angled sides of a right-angled triangle are a, b, and the hypotenuse is c, then a squared + b squared = c squared;

That is, the sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse.

If the three sides of the triangle a, b, and c meet a 2 + b 2 = c 2, for example: a right-angled side is 3, a right-angled side is 4, and the hypotenuse is 3*3+4*4=x*x, x=5. Then this triangle is a right triangle. (The inverse theorem of the Pythagorean theorem).

It's the same for both.

Civil science proves the Pythagorean theorem: Zhao Shuang and his Pythagorean diagram.

Pythagorean theorem: In China, the sum of the square of the two right-angled sides of a right triangle is equal to the square of the hypotenuse is called the Pythagorean code joke or Pythagorean chord.

The ancient Egyptians used knots to make the RT triangle theory, also known as the Pythagorean theorem or Pythagoras

theorem）。

Theorem: If the two right-angled sides of a right-angled triangle are a, b, and the hypotenuse is c, then a squared + b squared = c squared;

That is, the sum of the squares of the two right-angled sides of the right-angled triangle is equal to the square of the hypotenuse.

If the three sides of the triangle a, b, and c meet a 2 + b 2 = c 2, for example: a right-angled side is 3, a right-angled side is 4, and the hypotenuse is 3*3+4*4=x*x, x=5. Then this triangle is a right triangle. (The inverse theorem of the Pythagorean theorem).

It's the same for both.

The Pythagorean law is a special case of the cosine theorem at an angle a of 90°. Let the length of the three sides of any triangle be a, b, c, then there is a 2=b 2+c 2-2bccosa. The Pythagorean theorem, on the other hand, gives the angle a of a right triangle to be 90°.

then there is a 2 = b 2 + c 2. In fact, it is a 2 = b 2 + c 2-2bccos 90°.

The Pythagorean theorem is the relationship between the sides of a right triangle based on a right angle.

The cosine theorem is the relationship between sides and angles that can be applied to non-right triangles.