The Pythagorean theorem in junior high school. How to calculate the Pythagorean theorem in junior hi

The outer angles of the triangle are equal to the sum of his two angles that are not adjacent to each other.

The Pythagorean theorem is the key content of mathematics in the high school entrance examination, and it also plays a pivotal role in the future study of geometry. The calculation of the mathematical Pythagorean theorem is sorted out below, I hope it will be helpful to you.

In a right-angled triangle on a plane, the square of the lengths of the two right-angled sides adds up to the square of the hypotenuse lengths. 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 length of the side search shirt of c.

According to the Pythagorean theorem, a +b =c is 3 +4 =c, i.e., 9+16=25=c, c= 25=5. So we can use the Pythagorean theorem to calculate that the side length of c is 5.

The Pythagorean theorem is a basic geometric theorem that states that the sum of the squares of the two right-angled sides of a straight-spring 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.

1.The three positive integers that can form the three sides of a right triangle are called Pythagorean numbers, that is, when a, b, and c are positive integers, they are called a, b, and c are a set of Pythagorean numbers.

2.Memorizing the common Pythagorean numbers can increase the speed of problem solving, such as etc.

3.Expressed in an algebraic formula with letters: (n is a positive integer); (n is a positive integer); (m>n,m,n is a positive integer).

1.Because in RT ABC, ACB = 90°, AB = 13And because Cd is the midline on the hypotenuse AB, so Cd = Ad = Ab = 1 2AB = and because CE is the height of the hypotenuse Ab, so AC CB = Ab EC, EC = 60 13

In RT ace, AE=90°, so AE=25 so AE:ED:DB=50:

2.Make DF perpendicular to CB, hanging feet for.

Because Cd is the midline on the hypotenuse AB, Cd is equal to half of the hypotenuse, Cd = 1 2Ab = Ad = DB = 13 2

Because CE is the height of the hypotenuse AB, AC CB=AB EC, CE=60 13

In RT ace, AE= AC2-CE2=25 13ED=AD-AE=13 2-25 13=119 26AE:ED:DB=25 13:

Cut the cylinder along the high line with a knife, which is equivalent to a rectangle.

The height is 12cm, and the bottom radius is 3cm.

The length of the rectangle is the circumference of the bottom surface of the cylinder = 2 r = 2 * 3 * 3 = 18 cm (take 3 in the question).

The width of the rectangle is the height of the cylinder = 12 cm

Therefore, the ab distance is the diagonal length drawn in the figure = under the root number (9 + 12) = 15 cm, so the shortest distance that needs to be crawled is 15 cm

PS: After looking at the picture drawn by lz, I found that the previous one was written wrong, point B should indeed be at the middle point of the length, and the triangle is a right triangle composed of 9, 12, and 15.

Because the line segment between two points is the shortest.

Therefore, the side of the cylinder is formed into a rectangle, and the circumference of the ground with a length of 2 r = 2 * 3 * 3 = 18 and a width of 12 is 12

The shortest distance to crawl is squared equal to 18 squared plus 12 squared = 468, so the shortest distance is about.

Put the sides of the cylinder, then the distance the ant climbs over is the diagonal of the rear rectangle.

The width of the rectangle is the height of the cylinder, and the length is the circumference of the bottom surface of the cylinder.

Circumference = 2 r = 2 3 3 = 18 cm.

12 squared plus 18 squared = 468 under the root

Because the shape of the cylinder in this problem is rectangular:

Then the length of the rectangle obtained from the cylinder is: l=2 r=2x3x3=18cm, and the width of the rectangle obtained from the cylinder is: d=12cm

Ant on the bottom side of the cylinder ant, want to eat food at point B opposite the bottom of point a, even if the diagonal in the rectangle:

So l = (18x18+12x12) = 468

Be squared = square of AC + square of AE.

As shown in the figure: because de is the perpendicular bisector of bc, so be=ce because ace is a right triangle according to the pythagorean theorem ce squared = ac squared = ae squared be=ce so it is equal . Hope to adopt.

If E is on AC, the distance from the point to both ends of the line segment on the vertical bisector can be used to obtain BE=CE, because CE=(AC-AE), so the square of CE = the square of (AC-AE), and the square of CE = the square of AC + the square of AE+2AC*AE, so the square of BE = the square of AC + the square of AE + 2AC*AE, because AC and AE are both greater than 0, so the square of BE AC + the square of AE.

Do AE vertical BC on E

ac=ab, ae perpendicular bc, so be=ce

Angular bac = 90

So ae=be=ce=1 2bc

ad²=de²+ae²

ab²+ac²=（be+de）²+ce-cd）²=2（be²+de²）

2ad²

Flip the staircase out and make it a rectangle, and the carpet is at least one height and one length.

Length = 5 squared - 3 squared re-root number = 4

At least =3+4=7 meters.

The carpet is a rectangle, area = length times width = 2x7 = 14, it costs 14x30 = 420 yuan.

Using the Pythagorean theorem, the bottom is 4 meters, assuming that AB is straightened, the length of AB is equal to AB+CB, so the length of the carpet is 4+3=7m2 7 30 = 420, so this carpet costs 420 yuan.

The length of the ground occupied by the staircase is 4 meters, and because the staircase is 3 meters high, it is said that the height of each staircase adds up to 3 meters.

In the same way, the length is 4 meters, so a total of 7 meters 7 * 2 * 30 = 420 yuan.

Through the image translation, it can be seen that the carpet area in the horizontal direction a=5 2=10m In the same way, the carpet area in the vertical direction b=3 2=6m The total area s=6+10=16m

Therefore, it costs 16 30 = 480 yuan.

The length of the carpet is the sum of the two right-angled sides of the triangle, which is 7m

The area is 7 2 = 14m

Need 14 30 = 420 yuan.

Ground 4 carpet at least 7 meters 210 yuan.

A and b are not a number, a2+b2 is equal to a constant, this is a circle, the center of the circle is (0,0) The dots on the circle are the answers.