Right triangle and circle, what is called a right triangle

The distance from the center of the circle to the three sides is equal.

The equation for the ab line is y=2-2x

2x+y-2=0

Formula: The distance from the point (m,n) to ax+by+c=0 is the absolute value of [(am+bn-c) root sign (a 2 + b 2)].

The set point is (m,n), because the distance to the x and y axes is equal, and the absolute value of m=n(2m+m-2) root number (2 2+1 2)] is mm=2 (3-root number 5).

Coordinate. m=2 (3-root number 5), m=2 (3-root number 5)).

(1) Because the circumferential angle is equal to half of the central angle of the circle, the central angle of the "diameter" is 180 degrees, so the circumferential angle of the diameter is 90 degrees, so the diameter of the circle is one side, and the triangle with the vertex on the arc is a right-angled triangle. This is the inverse theorem of your statement.

2) As for explaining why "all" right-angled points of a right-angled triangle are on an arc. First of all, it is proved that all right triangles on the arc are right-angled, which has been explained in (1); Then explain that all triangles where the third point is not on the arc are not right triangles with right angles to the point at that point.

is the midpoint (i.e., the center of the circle) that connects this vertex to the opposite edge, which is the midline on this side.

It can be seen that the center line is equal to the radius of the circle and is equal to half of the side (diameter) on which it is located.

So the triangle is a right-angled triangle.

The question I want to ask is! What is the radius of a circle equal to that of a triangle? Urgent! Urgent! Urgent!

The two vertices are the endpoints of the diameter, and the triangle of the other vertex on the circle is a right triangle.

Because the diameter is already the longest in a circle, more than 90 degrees is an obtuse angle, but if the angle is obtuse, the angle must exceed the edge of the diameter, so it is impossible, and the acute angle is almost the same.

You connect that right-angled point to the center of the circle and it comes out.

No, the third point has to be on the circle to be true.

Relationship between circles and triangles:

1. Three points that are not on the same straight line determine a circle.

2. The circumscribed circle of the triangle: the circle that passes through the three vertices of the triangle.

3. The outer center of the triangle: the intersection point of the vertical bisector of the three sides of the triangle, that is, the center of the circumscribed circle of the angle of the Sanjing rock cover.

4. The inscribed circle of the triangle: the circle tangent to all three sides of the triangle.

5. The heart of the triangle: the intersection of the bisector of the three corners of the triangle, that is, the center of the inscribed circle of the triangle.

The closed curve formed by rotating around a point and at a distance of a certain length in a flat jujube plane is called a circle. In a plane, a circle is a set of points whose distance to a fixed point is equal to a fixed length is called a circle.

The circle is prescribed as 360°, which is the ancient Babylonians who moved a position about every 4 minutes when observing the rising sun on the horizon, and 360 positions in 24 hours a day, so the inner angle of a circle was prescribed to be 360°. This ° represents the sun.

A triangle is a closed figure composed of three line segments in the same plane that are not on the same straight line, which are connected sequentially, and have bright applications in mathematics and architecture.

Common triangles are divided into ordinary triangles (the three sides are not equal) and isosceles triangles (isosceles triangles with unequal waists and bases, and isosceles triangles with equal waists and bottoms, that is, equilateral triangles); According to the angle, there are right triangles, acute triangles, obtuse triangles, etc., of which acute triangles and obtuse triangles are collectively referred to as oblique triangles.

One day, Circle and Triangle meet, and they think each other looks special and decide to play a game together.

The circle and the triangle are mortal enemies, each of them has its own merits, and they quarrel endlessly, and neither of them is willing to show weakness. Yuan said, "I'm faster than you."

But the triangle said, "I can stand firm." "After they said that, they decided to race running and standing.

The run began, and the circle disappeared in the blink of an eye, and the triangle couldn't run, and his three corners were scarred. After a while, after Yuan came back from a lap, he saw that the triangle was still struggling on the starting line, Yuan laughed, and the triangle said unwillingly: "Don't be too proud, I'll let you see how good I am when I stand up."

Yuan said again: "Compare and compare, who is afraid of whom!" After that, the standing competition began, and I saw that the triangle was standing steadily, and the circle was still running as if it was running, and the old potato pie kept turning.

The triangle said proudly: "Yuan, you admit defeat, you can't stand firm." Yuan said

I can't stand on my feet, but you can't run fast. They quarreled with red faces and red ears, and no one was convinced.

The circle and triangle finally calm down and decide to cooperate. The circle said, "Triangle, you jump into my circle."

The triangle said, "Okay." They formed a new figure, and the circle ran around with the triangular hand, and the triangle said happily

I was finally able to run. So the triangle said to the circle, "You jump into my three sides."

Yuan said, "Okay. Then they formed a new figure, and the triangle was motionless, and the circle felt that it was standing firmly, and only the circle was heard

Great, I'm able to stand firm. ”

Circles and triangles understand a truth: to achieve wishes, sometimes it is not enough to rely on one's own strength, but also need the help of others.

Second grade: Li Xingyuan.

There is a triangle with an angle of 90 degrees called a right triangle. There are two types: ordinary right-angled triangles and isosceles right-angled triangles. I have brought you the relevant knowledge points of right triangles.

There is a triangle with an angle of 90 degrees called a right triangle. There are two types: ordinary right-angled triangles and isosceles right-angled triangles.

The right side of a right triangle is also called a "chord", and if the two right angles are not the same length, the short side is called a "hook" and the long side is called a "strand".

A right triangle is a special kind of triangle that has some special properties in addition to the properties of a general triangle:

Property 1: The sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse.

Property 2: In a right triangle, two acute angles are surplus to each other.

Property 3: In a right triangle, the midline on the hypotenuse is equal to half of the hypotenuse (i.e., the outer center of the right triangle is located at the midpoint of the hypotenuse, and the radius of the circumscribed circle r=c 2).

Property 4: The product of the two right-angled sides of a right-angled triangle is equal to the product of the hypotenuse and the height of the hypotenuse.

Property 5: The right-angled edge of an acute angle of 30 degrees is half of the hypotenuse.

1) The sum of the three internal angles of the triangle is equal to 180°;

2) One outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it;

3) One outer angle of the triangle is greater than any of the inner angles that are not adjacent to it;

4) The sum of the two sides of the triangle is greater than the third side, and the difference between the two sides is less than the third side;

5) Within the same triangle, the big side is against the big angle, and the big angle is against the big side.

Judgment 1: A triangle with an angle of 90° is a right triangle.

Judgment 2: If.

Then a triangle with a, b, and c as sides is a right-angled triangle with c as hypotenuse (the inverse theorem of the Pythagorean theorem).

Judgment 3: If the side of a triangle is half of one side at the 30° inner angle, then the triangle is a right-angled triangle with the long side as the hypotenuse.

Judgment 4: A triangle in which two acute angles are co-angles to each other (the sum of the two angles equals 90°) is a right triangle.

Judgment 5: If two straight lines intersect and the product of their slopes is negative to each other, then the two lines are perpendicular to each other. Then this triangle is a right triangle.

A triangle with a corner at right angles is called a right triangle.

In a right-angled triangle, the two sides adjacent to the right angle are called right-angled edges, and the edges opposite by right-angled angles are called hypotenuses. The sides of a right triangle are also called "chords". If the two right-angled sides are not the same length, the short side is called the "hook" and the long side is called the "strand".

Question: There are several degrees of right triangles.

Question: There are two types.

There is a triangle with an angle of 90°, and there are two types: ordinary right triangle and isosceles right triangle.

One of the triangles with a right angle (90 degrees) is called a right triangle.

One of the inner angles of the triangle is 90°, which is a right triangle.

One angle of a triangle is 90 degrees and is called a right triangle.

Yes? Isn't there a triangle with an angle of 90°?

The circumferential angle on the diameter is a right angle.

Because the circumferential angle of the diameter is a right angle.