How to do the Pythagorean theorem? How is the Pythagorean theorem used?

Uh-huh, that makes sense.

You can also square the root number to do the problem.

This avoids the root number

The Pythagorean theorem is about a right triangle, knowing the formula for finding the length of the third side of any two sides. Set the right angles to call the old edges A and B respectively, and the hypotenuse side is C.

a a+b b=c c, I remember giving an example when I talked about the Pythagorean theorem.

The two right-angled edges are 3 and 4 respectively.

3×3+4×4=c²

c²=9+16=25

c=5 Similarly, if you know a straight and a straight and ascension angle, the edge and the hypotenuse are found on the other side.

b²=c²-a²

b²=5²-3²=25-9=16b=4

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.

As shown in the figure below, i.e., a + b = c ).

Example: For example, in the right triangle of the figure above, 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 = 25 = 5

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

Extended content: Pythagorean theorem:

The Pythagorean theorem, also known as the quotient theorem, Pythagorean theorem, Pythagorean theorem, and Pythagorean theorem, is a fundamental 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 the previous condition, then the formula only satisfies c is an acute angle).

Evidence 1 (Zou Yuanzhi Zheng Pei Chaoming) Fighting.

Make four congruent triangles with a and b as the right-angled side and c as the hypotenuse, and put them together as shown in the figure below to make a, e, and b three-point collinear, b, f, and c three-point collinear, and c, g, and d three-point collinear.

rt-haert△ebf

2 AHE = ZBEF

2. AHE + ZAEH = 90 ° .zbef+zaeh=90°"a, e, and b are collinear.

zhef = 90°, and the quadrilateral efgh is a square.

Since the four right-angled triangles in the above figure are congruent, it is easy to obtain that the quadrilateral ABCD is a squareThe area of the square ABCD = the area of the four right triangles + the area of the square EFGH with the silver file. ".

a+-b) 2=4(1 2) -ab+c 2, arranged to obtain a 2 + b 2 = c 2

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 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. In China, Shang Gao during the Shang Dynasty proposed a special case of the Pythagorean theorem of "Pythagorean Three Strands, Four Xuanwu".

In the West, the Pythagoreans of ancient Greece in the 6th century BC were the first to propose and prove this theorem, who used the deductive method to prove that the square of the hypotenuse of a right triangle is equal to the sum of the squares of two right angles.

The Pythagorean theorem is used to solve a right triangle in :

Know any two sides and find a theorem for the third side. (C is the hypotenuse A and B right-angled edges).

c^2=a^2+b^2

a^2=c^2-b^2

b^2=c^2-a^2

It is also sometimes used to determine whether a triangle is a right triangle.

For example, if the three sides of a triangle are known, it proves that the triangle is not a right triangle.

Proof: Because 3 2 + 4 2 = 5 2

So this triangle is a right-angled triangle.

Answer: The Pythagorean theorem is a basic geometric theorem that states that the sum of the squares of the sides of two right-angled sides of a right triangle (i.e., "Hook", "strand") is equal to the square of the side lengths of the hypotenuse (i.e., "strings"). That is, if the two right-angled sides of a right-angled triangle are a and b, and the hypotenuse is c, then a +b = c. The Pythagorean theorem has now found about 400 ways to prove it, making it one of the most provable theorems among mathematical theorems.

The Pythagorean number forms a positive integer array (a,b,c) of a +b = c. (3,4,5) is the Pythagorean number.

The Pythagorean theorem is an elementary geometric theorem, 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. "Pythagorean three, strand four, string five" is one of the most famous examples of the Pythagorean theorem. When the integers a,b,c satisfy the condition a +b = c, (a,b,c) is called the Pythagorean array.

That is, if the two right-angled sides of a right-angled triangle are a and b, and the hypotenuse is c, then a +b = c. "Common Pythagorean numbers are (3, 4, 5), (5, 12, 13), (6, 8, 10).

The sixteen proof methods of the Pythagorean theorem are the basis for the proof of mathematical geometry in junior high school, in order to lay the foundation for better learning the proof of the Pythagorean theorem, I will share the sixteen proof methods below.

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Pythagorean theorem: Pythagorean four strings five.

The details are as follows:

1) The Pythagorean theorem applies to right triangles;

2) The two right-angled sides of a right-angled triangle, one right-angled side is 3 in length and the other is 4 in length, then, there must be hypotenuse with a length of 5.

3) According to the calculation method of triangle side length, the length of the hypotenuse = the sum of the squares of the two right-angled sides. That is:

Under the root number (3 +4) = under the root number (25) = 5

It coincides with the Pythagorean theorem.