The Concept of a Triangle 10, The Concept of a Triangle

The Cartesian coordinate system is established with the center of the semicircle as the original center.

Because the radius is.

The equation is: x 2 + y 2 = > = 0).

The truck must walk through the middle.

Let x=, then y 2=>

So it can be passed.

Symmetrical the axis of this diagram gives us a circle with a radius of meters, and the question becomes whether a rectangle with a height of meters and a width of 3 meters can be passed through the circle.

Calculate the diagonal length of the rectangle, add the square of 3 and then open the square, about meters, less than the diameter of the circle in meters, so it can be passed.

Absolutely original!!

First draw a plane Cartesian coordinate system, take the origin as the center of the circle, draw a circle for the radius, this car is the easiest to pass through in the tunnel, so x=, substitute the equation of the circle x 2 + y 2 =, solve y, get the y in contrast, if it is greater than you can pass.

OK. At a height of meters, the tunnel width is:

3 meters.

OK! Square square = square of >.

So it can be passed.

OK. Open from **.

The high Pythagorean theorem yields an hypotenuse of about <

Therefore it can be passed.

Absolutely. The radius is meters, indicating that the bottom surface of the tunnel is meters wide.

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.

A closed shape consisting of three line segments that are not on the same line is connected one after the other, called a triangle. Problems for elementary school students.

Triangle definition: A closed interior angle and a geometric figure of 180 degrees obtained by three line segments in the same plane and not on the same straight line, which are connected one after the other.

Common triangles are divided into isosceles triangles (isosceles triangles with unequal waists and bases, isosceles triangles with equal waists and bottoms, i.e., equilateral triangles), and unequal 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.

.The triangle has a total of six hearts: the intersection of the three angular bisectors, which is also the center of the inscribed circle of the triangle.

Properties: Equal distance to three sides. Outer Heart:

The intersection of the three perpendicular lines is also the center of the circumscribed circle of the triangle. Properties: Equal distances to the three vertices.

Center of gravity: The intersection of the three midlines. Nature:

The distance from the third of the three midlines to the vertex is 2 times the distance to the midpoint of the opposite side. Vertical Center: The intersection of the three heights of the straight line.

Properties: This point is divided into two parts of each high line multiplied by the side center: the intersection of the outer bisector of any two corners of the triangle and the inner bisector of the third corner

The distance to the three sides is equal. Centroid: Divides the perimeter of the triangle into 1:

The intersection of a straight line and one side of a triangle of 1. Properties: A triangle has three centrios, and three straight lines connected to the vertices of the triangle meet at one point.

Euler line: The outer center, center of gravity, nine-point circle center, and vertical center of the triangle are located on the same straight line in turn, and this straight line is called the Euler line of the triangle.

I'll do it first, and I'll do it first, and I'll be in the truth.

By a vertex, two to one to one corner to one corner.

A closed graphic enclosed by three line segments.

The common three-sided early angle is divided into ordinary triangles (the three sides are not equal), isosceles triangles (isosceles triangles with unequal waists and bottoms, and isosceles triangles with equal waists and bottoms, that is, equilateral triangles); According to the angle, there are right-angled triangles, acute triangles, obtuse triangles, etc., among which acute triangles and obtuse triangles are collectively referred to as oblique triangles.

Judgment: 1. The three sides corresponding to the two triangles are equal, and the two triangles are congruent, referred to as "Bianbianbian" or "SSS"."。

2. The two sides of the two triangles and their angles are equal, and the two triangles are congruent, referred to as "corner edges" or "SAS".

3. The two corners corresponding to the two triangles and their intersections are equal, and the two triangles are congruent, referred to as "corners" or "ASA".

Concept: 1. The sum of the internal angles of a triangle on a plane is equal to 180 degrees.

2. The sum of the outer angles of the triangle on the plane is equal to 360 degrees.

3. On the plane, the outer angles of the triangle are equal to the sum of the two inner angles that are not adjacent to it.

4. At least two of the three inner angles of a triangle are acute.

5. At least one angle in the triangle is greater than or equal to 60 degrees, and at least one angle is less than or equal to 60 degrees.

6 .The sum of any two sides of the triangle is greater than the third side, and the difference between any two sides is less than the third side.

7. In a right-angled triangle, if an angle is equal to 30 degrees, the right-angled side opposite by the 30-degree angle is half of the hypotenuse.

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

9. The middle line of the hypotenuse of a right triangle is equal to half of the hypotenuse.

10. The three angular bisector lines of the triangle intersect at one point, the straight leakage and disturbance lines of the three high lines intersect at one point, and the three middle lines intersect at one point.

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

12.Triangles of equal base and height are equal in area.

13.The ratio of the area of a triangle with equal bases is equal to the ratio of its height, and the ratio of the area of a triangle with equal height is equal to the ratio of its base.

14.Any one of the midlines of the triangle divides the triangle into two triangles of equal size.

15.The angular bisector of the top corner of an isosceles triangle is in a straight line with the high on the base edge and the middle line on the bottom edge.

Definition of Triangle:A closed figure consisting of three orange segments that are not on the same line is connected one after the other, which is called a triangle. The figure enclosed by three straight lines on the plane or three arcs on the sphere, and the figure enclosed by the three straight lines is called a plane triangle; The shape enclosed by three arcs is called a spherical triangle, also known as a trilateral.

1. Classification of triangles:

1. Divide by angle:

1) Judgment method 1:

Acute triangles: The three inner angles of the triangle are all less than 90 degrees.

Right Triangle: One of the three inner angles of a triangle is equal to 90 degrees and can be denoted as RT.

Obtuse triangle: One of the three inner angles of a triangle is greater than 90 degrees.

2) Judgment method 2:

Acute triangle: The largest of the three inner angles of a triangle is less than 90 degrees.

Right Triangle: The largest of the three inner angles of a triangle is equal to 90 degrees.

Obtuse triangle: The maximum angle of the three inner angles of the triangle is greater than 90 degrees, and the front of the triangle is less than 180 degrees.

2. Divide by side:

1) Unequal triangle: A triangle with three unequal sides.

2) Isosceles triangle: An isosceles triangle refers to a triangle with equal sides.

3) Equilateral triangle: Equilateral triangle (also known as regular triangle) is a triangle with three equal sides, and its three internal angles are equal, all of which are 60°, which is a kind of acute triangle.

IIThe role of triangles:

The stability of the triangle makes it not easy to deform like a quadrilateral, and it has the characteristics of stability, solidity, and pressure resistance. Triangular structures have a wide range of engineering applications. Many of the buildings are triangular in shape, such as the Eiffel Tower, the Egyptian pyramids, and many more.

Triangle Determination Theorem and Perimeter Formula:

1. Determination theorem:

1. The three sides corresponding to the two triangles are equal, and the two triangles are congruent, referred to as "edge edge edge" or "sss";

2. The two sides of the two triangles and their angles are equal, and the two triangles are congruent, referred to as "corner edges" or "SAS".

3. The two corners corresponding to the two triangles and their intersections are equal, and the two triangles are congruent, referred to as "corners" or "ASA".

4. The two corners corresponding to the two triangles and the opposite side of one of the corners are equal, and the two triangles are congruent, referred to as "corner edges" or "AAS";

5. One hypotenuse and one right-angled side corresponding to two right-angled triangles are equal, and the two right-angled triangles are congruent, referred to as "hypotenuse, right-angled side" or "hl";

Note: "Edges" i.e. "SSA" and "Corners" i.e. "aaa" are false proof methods.

Second, the perimeter formula:

If the three sides of a triangle are a, b, and c, then c=a+b+c.