Equation 30 of the Pythagorean theorem in geometry

a2 + b2 = c2

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.

Popularize. If the hypotenuse of a right-angled triangle is regarded as a vector on a two-dimensional plane, and the two hypotenuse sides are regarded as projections on the coordinate axis 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.

The sum of squares of the right-angled edges is equal to the square of the hypotenuse, if the right-angled edges are a, b, and the hypotenuse is c.

a^2+b^2=c^2

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

Is that it? ：2 2 2

a+ b = c 2 represents the square of the letters below.

The Pythagorean theorem is one of the most basic theorems in triangles and an important part of junior high school mathematics, it is a mathematical formula used to calculate the relationship between the lengths of each side in a right triangle. The formulation of the Pythagorean theorem is that the square of the hypotenuse is equal to the sum of the squares of the two right-angled sides.

The mathematical formula for the Pythagorean theorem is as follows:

Let the two right-angled sides of a right-angled triangle be a and b respectively, and the hypotenuse is c, then there is:

c² =a² +b²

where " " is squared, i.e., a number multiplies itself once.

The meaning of this formula is that for any right triangle, if we know the length of two right sides, then we can use the Pythagorean theorem to calculate the length of the hypotenuse.

For example, if the right-angled sides of a right-angled triangle are 3 and 4, respectively, then the length c of the hypotenuse can be calculated using the Pythagorean macro-cons positive theorem:

c² =3² +4² =9 + 16 = 25

Therefore, c = 25 = 5

There are many ways to prove the Pythagorean theorem, the most famous of which is Euclid's. Euclid proved the Pythagorean theorem by splitting a right triangle into two parallelograms and a square, and then deriving the formula of the Pythagorean theorem geometrically.

In addition to Euclidean proofs, there are many other proof methods, such as algebraic proofs, geometric proofs, similar triangle proofs, and so on.

In practical applications, the Pythagorean theorem can be used to solve many problems related to right triangles, such as measuring the height of objects that cannot be directly measured, calculating the tilt angle of buildings, calculating the resistance in electrical circuits, and so on. Therefore, it is very useful to learn the Pythagorean theorem.

In conclusion, the Pythagorean theorem is one of the most fundamental theorems in triangles, which provides a mathematical formula for calculating the relationship between the lengths of each side in a right triangle. It is very important for junior high school mathematics students to learn the Pythagorean theorem, which not only helps to improve mathematical literacy, but also helps to apply mathematical knowledge to solve practical problems.

Pythagorean theorem: In a right-angled triangle on a plane, the square of the length of the two right-angled sides adds up to the square of the hypotenuse length. Example:

If the side length of a is 3 and the side length of b is 4, then we can use the Pythagorean theorem to calculate the side length of c. From the Pythagorean theorem, a + b = c 3 +4 = c, i.e.: 9 + 16 = 25 = c , c = 5.

So we can use the Pythagorean theorem to calculate that the side length of c is 5.

The Pythagorean theorem, also known as the quotient theorem, the Pythagorean theorem, the Pythagorean theorem, and the Hundred Bull theorem, is a basic and important theorem in plane geometry. The Pythagorean theorem states that the sum of the squares of the lengths of the two right-angled sides of a right-angled triangle on a plane (known as hook length, strand length) is equal to the square of the hypotenuse (chord length). Conversely, if the sum of the squares of the two sides of a triangle on a plane is equal to the square of the length of the third side, then it is a right triangle (the side opposite the right angle is the third side).

The Pythagorean theorem is one of the important mathematical theorems discovered and proven by mankind in the early days.

The inverse theorem of the Pythagorean theorem:

The inverse theorem of the Pythagorean theorem is a simple way to determine whether a triangle is obtuse, acute, or right-angled, where ab=c is the longest side:

If a + b = c then abc is a right triangle.

If a + b > c then abc is an acute triangle (if ab=c is the longest side without previous conditions, then the formula only satisfies c is an acute angle).

If A +B "Guess Hui C", then abc is an obtuse triangle.

The formula for the Pythagorean theorem is a +b = c , and in a right-angled triangle on a plane, the square of the length of the two right-angled sides adds up to the square of the hypotenuse length. If the length of the two right-angled sides of a right-angled triangle is a and b, and the length of the hypotenuse is c, then the Pythagorean theorem can be used.

If the side length of A is 3 and the side length of B is 4, then we can calculate the side length of C using the Pythagorean fixed hand empty method. From the Pythagorean theorem, a + b = c 3 + 4 = c, i.e., 9 + 16 = 25 = c , c = 5.

So I can use the Pythagorean theorem to calculate that the side length of c is 5.

In addition, the inverse theorem of the Pythagorean theorem can also be used to determine whether a triangle is a right angle, an acute angle, or an obtuse triangle. where ab=c is the longest side, and if a +b =c, then abc is a right triangle. If a +b > c then abc is an acute triangle (if ab=c is the longest side without the previous condition, then the formula only satisfies c is an acute angle).

1. Pythagorean theorem: In a right-angled triangle on a plane, the square of the length of the two right-angled sides adds up to the square of the length of the hypotenuse. For example, if the length of the side of a is 3 and the length of the side of b is 4, then we can use the Pythagorean theorem to calculate the length of the side of c.

2. In ancient China, the right triangle was called the Pythagorean shape, and the smaller of the right-angled sides was the hook, and the other long right-angled side was the strand, and the hypotenuse was the chord.

What is the formula for the Pythagorean theorem.

Hello answer, I have seen your question and am sorting out the answer, please wait a while Hello, the Pythagorean theorem formula is that the square of a plus the square of b is equal to the square of c. If the two right-angled sides of a right-angled triangle are a, b, and the hypotenuse is c, then the formula is: a2+b 2=c 2.

The Pythagorean theorem now has about 500 ways to prove it, making it one of the most provable theorems in mathematics. The Pythagorean theorem is one of the important mathematical theorems discovered and proven by mankind in the early days, one of the most important tools for solving geometric problems with algebraic ideas, and one of the links between numbers and shapes.

The Pythagorean theorem is a fundamental geometric theorem that 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. In ancient China, the right triangle was called the Pythagorean shape, and the smaller of the right-angled sides was the hook, the other long right-angled side was the strand, and the hypotenuse was the chord, so this theorem was called the Pythagorean theorem, and some people called the Shanggao theorem.

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 a, b, and c are used to represent the two right-angled sides and hypotenuse sides of a right triangle, respectively, then a2+b 2=c 2,3 squared plus 4 squared = 9 + 16 = 25 = 5 squared 4 squared plus 7 squared 16 + 49 = 65

The length of the other side = root number 65

The sum of the squares of two right-angled sides in the Pythagorean theorem is equal to the square of the hypotenuse.

It is inherently difficult to prove that the hook is three strands, four strings and five.

a2+b2=c2, the hypotenuse is the root number 4 square plus 7 square.

It is the root number 65

The formula of the Pythagorean theorem is 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, let the right-angled side be a, b, and the hypotenuse is c with the square of c = the square of a + the square of b because the other two angles are 45 degrees, so it is an isosceles right-angled triangle, the sum of two isosceles is 5700, and one is 5700 2 = 2850 meters.

From the Pythagorean theorem, there is the square of the hypotenuse = the square of 2850 + the square of 2850, so the hypotenuse is 2850 times the root number 2

The perpendicular line h of the hypotenuse of 2 can be obtained from the area, the area of the triangle = 1 2 * 2850 * 2580 = 1 2 * 2850 times the root number 2 * h

h=2850 root number 2 = 1425 times root number 2

The formula of the Pythagorean theorem: the three sides are a, b, and c, where c is the hypotenuse, and a and b are right-angled edges, then a 2 + b 2 = c 2

In this problem, if a and b are both 5700 meters, then the length of the right angled side, that is, the hypotenuse, is 5700* (root number 2), which can be found directly by substituting the formula of the Pythagorean theorem.

Find the length of the perpendicular line: set the high position h of the hypotenuse, then c*h 2=a*b 2, and substitute the data to find h=5700 (root number 2) = 2850 * (root number 2), which is the direct use of the area formula: area = (bottom * height) 2.

1.The formula of the Pythagorean theorem: the square of a + the square of b = the square of c a and b are two right-angled edges, and c is the side opposite the right angle, that is, the hypotenuse.

The sum of the squares of 5700 + the squares of 5700 is the length of the side opposite by the right angle2Use the equal area method.

The length of the perpendicular line multiplied by the length of the right-angled side = the product of the two right-angled edges to solve the equation.

A +b = C (a, b are right-angled edges, c is hypotenuse) 5700 +5700 square root 8061 meters perpendicular length = 4500 * 4500 * divided by 8061 1256 is to use the area to find the height.

The length of the side opposite at right angles is: root number (5700 2 + 5700 2) = 300 root number 722

The length of the perpendicular line can be calculated by the area, set to x, and the area of the triangle is 5700*5700*1 2=300 root number 722*x

x = 150 root number 722

The formula of the Pythagorean theorem is A2+B2=C2 (a,b is the right-angled edge, c is the hypotenuse).

The length of the opposite side at a right angle is: 5700 * root number 2 = meters.

The length of the vertical line made at right angles is: 5700 roots, number2 = meters.

The formula of the Pythagorean theorem: A2 + B2 = C2 (A and B are two right-angled edges, C is the hypotenuse).

Pure manual calculation,The second question really can't come up with it.,After all, it's been 5 years since I graduated from college.,It's not enough brains to do questions at night.,Haha,I'm thinking about it tomorrow.,Come out and add it.,But I think the answer stolen from the homework gang upstairs The second question can't directly explain the four points of the circle.。