The Pythagorean theorem about isosceles right triangles

Let the isosceles right triangle made with AB as the side.

The area is S1, the area of an isosceles right triangle made of AC is S2, and the area of an isosceles right triangle made of BC is S3.

i.e. 1 2ab ab + 1 2ac ac 1 2bc bc so ab 2 + ac 2 = bc 2

Therefore, BC is an hypotenuse.

The angle A is a right angle, and the triangle ABC is a right triangle.

For example, the isosceles right-angled triangle made with each side as the hypotenuse of the triangle can be proven.

The trilateral ratio of an isosceles right triangle is: 1 to 1 to 2

Example: Known: Isosceles right triangle ABC

ab=ac, the point d is the midpoint of ac, the point e is the moving point of the bc edge, find the minimum value of ae+ad.

Solution: In the formula ae+ad, ad is a fixed value (half of the right-angled side ac), so when ae is the smallest, this sum is also the smallest. According to the "shortest perpendicular segment", when AE BC, AE is the shortest, which is easy to obtain AE equal to half of BC.

Let ab=ac a, then bc (ab 2 ac 2) = 2*a, ae 2 2*a, and ad 1 2*a

So the minimum value of AE+AD is 2 2a 1 2*a ( 2+1)a 2

Suppose a triangle is isosceles rt abc, and the condition tells you: acb=90°, cab=45°

Draw a picture for yourself and see).

Isosceles RT ABC

abc=180°-∠cab-acb

abc=∠cab

ac=bc (equiangular to equivalent).

When AC is 1, BC is also 1

ab²=ac²+bc²

ab = 2 This is the proof.

When you are done, you can see that one of the angles of a right-angled triangle is 45°, and the other angle is of course 45°, so the two right-angled sides are equal. This right triangle is an isosceles right triangle.

Conversely, if it tells you that it is an isosceles right triangle, then both angles are 45°!

If a question tells you about hypotenuse.

You can make one of the right-angled edges x, and since it's isosceles, both right-angled sides are x

e.g. hypotenuse = 5 2

Then x +x = (5 2).

2x²=50

x²=25x=5

Tired of fighting! Give it the best.

Set the isosceles right-angled three noisy rolling clear angles made with AB as the side.

The area is S1, the area of an isosceles right triangle made of AC is S2, and the area of an isosceles right triangle made of BC is S3.

i.e. 1 2ab ab + 1 2ac ac 1 2bc bc so ab 2 + ac 2 = bc 2

So BC is the hypotenuse, angle A is the right angle, and the triangle ABC is the right triangle.

For example, the isosceles right-angled triangle made with each side as the hypotenuse of the triangle can be proven.

Triangular natureAn isosceles right triangle is a special isosceles triangle.

There is an angle that is a right angle), and it is also a special right triangle (two right angled sides, etc.), so an isosceles right triangle has all the properties of an isosceles triangle and a right triangle (like a trilinear combination.

1. The Pythagorean theorem, the hypotenuse midline theorem of a right triangle.

etc.). Of course, isosceles right triangles also have the properties of general triangles, such as the sinusoidal theorem.

Cosine theorem, angular equinox and the front line of the fixed theorem.

Midline theorem, etc.

Isosceles right triangleThe Pythagorean theorem isBeveled edgesThe square is equal to 2 times the right-angled side of the stool called squared. An isosceles right triangle is a triangle with two 45 degree angles, so the hypotenuse is equal to the length of the waist of 2 times, and the content of the Pythagorean theorem is easy to be that the hook square plus the strand square is equal to the chord square, then the two right angles of the isosceles right triangle can be called the hook and the tenuse hypotenuse respectively called the chord.

Features of the Pythagorean theorem of isosceles right trianglesThe Pythagorean theorem is a basic geometric theorem, which refers to the sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse, ancient China called the right-angled triangle Pythagorean, and the smaller of the right-angled sides is the hook, and the other long right-angled side is the hypotenuse of the string, so this theorem is called the Pythagorean theorem, and some people call it the Shanggao theorem.

There is a special relationship between the three sides of the isosceles thick rounded right triangle, the square of the hypotenuse is equal to the sum of the squares of the two right angles, through the reproduction of history, so that students can feel the generation process of the Pythagorean theorem in the long river of history, understand the mathematical knowledge in life, and cultivate students' good habits of exploring knowledge in life.

Hello classmates, the Pythagorean theorem of isosceles right triangles refers to:

In a right-angled triangle, if the two right-angled sides are equal in length (i.e., isosceles), the hypotenuse is an open square multiple of the side length.

The specific formula is as follows: let the length of the right-angled side of the right-angled triangle be a, and the length of the hypotenuse is c, then there is: c = a 2

This means that if the length of the two right-angled sides of a right-angled triangle is equal, then the length of the hypotenuse is equal to the length of the right-angled side multiplied by 2. This theorem can be used to solve for unknown side lengths in isosceles right triangles.

The Pythagorean theorem applies to right triangles and of course to isosceles right triangles.

When the right-angled side of an isosceles right-angled triangle is 1, the hypotenuse is equal to the root number 2

When the hypotenuse of an isosceles right triangle is 1, the right side is equal to the root number of 2

The Pythagorean theorem applies to right triangles, and of course isosceles right triangles

Of course it does. And pick it up and use it, 1:1: root number 2

The Pythagorean theorem can be used: if the two right-angled sides of a right-angled triangle are a, b, and the hypotenuse is c, then a+b = c. An isosceles right triangle is also a special right triangle because one of the corners is a right angle, so the isosceles right triangle has all the properties of a right triangle.

The Pythagorean theorem, is a basic 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 methods of proving the scheme, which is one of the theorems with the most proof methods among the mathematical theorems. 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 Zhou Dynasty proposed a special case of the Pythagorean theorem of "Pythagorean three, four strings, five". In the West, the Pythagoreans of ancient Greece in the 6th century BC were the first to propose and prove this theorem, and they 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.

Nonsense! An isosceles right triangle is a type of geometric figure that does not belong to propositions, what does it prove?

All right triangles obey the Pythagorean theorem. Definition: In a right-angled triangle on a plane, the sum of the squares of the lengths of the two right-angled edges with the base is equal to the square of the hypotenuse lengths.

If the length of the two right-angled sides of a right-angled or triangular triangle is a and b respectively, and the length of the hypotenuse is c, then it can be expressed mathematically:

It is also known as Shang Gao's theorem (Western Zhou), Zhao Shuang's string diagram (Three Kingdoms), Pythagorean square diagram (nine chapters of arithmetic), Bainiu's theorem (ancient Greece), and Pythagorean theorem (ancient Greece).

eg:

For 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

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 bottom line of the isosceles right-angled triangular ridge destroys the hall, that is, its hypotenuse, which is equal to 2*right-angled edges.

This is also the result of the Pythagorean theorem: Yu Chun [(right-angled edge) 2+(right-angled edge) 2]= Sakurakuin 2*right-angled edge.