The perimeter area of the triangle is bisected by 10

The five hearts of the triangle.

The intersection of the three middle lines of the triangle at a point where the distance from the vertex is twice the distance from it to the opposite side, and the intersection point is called the center of gravity of the triangle, and the above theorem is the center of gravity theorem.

Outer Centroid Theorem The perpendicular bisector of the three sides of a triangle intersects at one point, which is called the outer center of the triangle.

Perpendicular theorem The three high intersections of a triangle at one point, which is called the vertical center of the triangle.

Inner Theorem The bisector of the three inner angles of a triangle intersects at one point, which is called the inner part of the triangle.

Paracentric Theorem The intersection of one of the inner bisectors of a triangle with the outer bisector of the other two vertices is called the paracentricity of the triangle. The triangle has three paracentricities.

From these definitions of "mind", a number of important properties can be obtained:

1) The area of the three triangles formed by the center of gravity and the line connecting the three vertices is equal;

2) the distance between the three vertices of the outer heart sweep is equal;

3) Vertical center and three vertices: any one of the four points is the vertical center of the triangle formed by the other three points;

4) The distance between the inner and the side to the three sides is equal;

5) The vertical center is the heart of the triangle composed of three vertical feet, or in other words, the heart of the triangle is the vertical center of the triangle next to it;

6) The outer center is the vertical center of the midpoint triangle;

7) The center is also the center of gravity of the midpoint triangle;

8) The outer center of the triangle at the midpoint of the triangle is also the outer center of its perpendicular triangle.

For the understanding of the "five hearts" of triangles, I hope you will first understand the definitions and theorems in the books, and then train the thinking habit of finding characteristics according to the definitions in the process of practice, summarize more by yourself, and gradually improve your ability to solve complex geometric problems.

So it's the center of gravity.

The center of gravity is made on the triangle with three highs, and the three highs must be in the heart

The high line divides the triangle, and there are three pairs of right-angled triangles, and there are twelve right-angled triangles, forming six pairs of similar shapes.

The center of gravity is the intersection of the three middle lines of the triangle.

Let the length and width of the rectangle be a and b, respectively, and the diagonal of the rectangle is c, and the circumference of 0< c rectangle is s=2a+2b

The circumference of the triangle l=a+b+c, add a+b on both sides and in the middle of equation (1), get a+b so s 2

You must know the side length of the rectangle.

The perimeter of the triangular type.

Definition: l=a+b+c

Formula: l=2s r (s is the area of the triangle, r is the radius of the inscribed circle of the triangle) the area of the triangle.

s=(a*b)/2

The formula for finding the third side of a right triangle.

The sum of the squares of the two sides is equal to the square of the hypotenuse.

Intersection of the angular bisector.

Xian Minrang drew the figure, and this conclusion was that any straight line does not need to cross a triangle.

vertices. Then connect the 3 vertices with the heart.

Then the distance from the heart to each side is equal, so that the area of any side of the line is the product of the circumference of that side (e.g., the left part of the triangle of the branch) and the distance from the heart to the side by half the heart.

Since the perimeter is bisected, the area is divided equally.

I don't know if you can understand the bridge-limb bureau?

3, one on each side, divides the triangle into two parts, one is a triangle and one is a quadrilateral.

The following one is definitely true:

Let's see if there are any articles 2 and 3. Thinking.

Here's how to do the ruler of x:

As a result, only one line segment exists at the same time dividing its perimeter and area.

Heart. First of all, it can be proved that as long as a straight line in the heart is divided into circumference, it will inevitably divide the area, draw a diagram, because of the heart, so their height is the same, which is not a triangle, and the area of several triangles can be divided into several triangles to calculate the area of the heart connected to the vertex, because their height is the same, they are the radius of the inscribed circle, so the area is only related to the perimeter, so the bisecting circumference must bisect the area, and it can also be proved that the bisecting area ratio of a straight line in the heart must also bisect the perimeter. They are competing with each other for conditions.