How many points of a triangle, how many center points does a triangle have?

1. Outside the heart. Triangle.

The center of the outer circle is referred to as the outer center. Closely related to the outer center are the central angle theorem and the circumferential angle theorem.

Second, the center of gravity. The intersection of the three middle lines of a triangle is called the center of gravity of the triangle. Mastering the center of gravity will be each.

The middle line is divided into a fixed ratio of 2:1 and a formula for the length of the middle line, which is easy to solve.

3. Hang your heart. The battle of the triangle is three high, called the vertical center of the triangle. The four equal (external) circular triangles formed by the vertical center of the triangle provide us with great convenience in solving the problem.

Fourth, the heart. The center of the triangle inscribed circle is simply called the heart. For the heart, to master the tension angle formula, it is also necessary to remember the following extremely useful equilibrarian relation:

Fifth, the side. One of the inner bisectors of a triangle intersects the outer bisectors of the other two inner angles.

One point, which is the center of the circle of the side cut circle, is called the side center. The side heart is often associated with the heart, and the side heart is also closely related to the half circumference of the triangle.

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The five hearts of the triangle refer to:

Heart: The heart is the center of the inscribed circle; The distance from the heart to the three sides is equal; The inner is the intersection of the bisector of the 3 inner angles.

Outer center: The outer center is the center of the circumscribed circle; The three vertices from the outer center to the triangle are equally distanced; The outer center is the intersection of the perpendicular lines of the 3 sides.

Center of gravity: 3 midline intersections. Several properties of the center of gravity:

1. The ratio of the distance from the center of gravity to the vertex and the distance from the center of gravity to the midpoint of the opposite side is 2:1.

2. The area of the three triangles composed of the center of gravity and the three vertices of the triangle is equal.

3. The sum of squares of the distance from the center of gravity to the three vertices of the triangle is the smallest.

4. In the planar Cartesian coordinate system, the coordinates of the center of gravity are the arithmetic mean of the vertex coordinates, that is, the coordinates of the center of gravity are (x1+x2+x3 3, y1+y2+y3 3).

Perpendicular: The intersection of perpendicular lines made from 3 vertices to 3 sides.

The acute triangle is perpendicular to the inside of the triangle; The right triangle is perpendicular to the right vertex of the triangle; The obtuse triangle is perpendicular to the outside of the triangle. The triangle has three vertices, three vertical feet, and the seven points in the center of the triangle can give six four-point circles.

Side: The intersection of 2 outer bisectors and one inner bisector. The center of a triangle's atangent circle (a circle tangent to one side of the triangle and the extension lines on the other two sides) is called a paracentric.

It is at an equal distance to the three sides. A triangle has three paracentricities, and it must be outside the triangle.

There are four distributions:

1. Five points in a straight line: 0;

2. Four of the five points are in the same straight line: 6;

3. Three of the five points are collinear.

7 cavity changye;

4. There is no arbitrary three-point collinear in the five points: 10.

Therefore, five dots can form 6 + 7 + 10 = 23 triangles.

1. Center of gravity: the intersection of the three midlines of the triangle.

2. External heart. The perpendicular bisector of the three sides of a triangle.

Intersection. 3. Perpendicular center: The three high intersections of the triangle are at one point.

4. Heart: The bisector of the three inner angles of the triangle intersects at one point.

5. Center: Only if the triangle is a regular triangle.

The center of gravity, the vertical center, the inner heart, and the outer heart are united into one heart, which is called the center of the regular triangle.

Characteristics of the five hearts of the triangle:

1. Heart: the intersection of the three bisectors of the inner angles of the triangle, that is, the center of the inscribed circle. The inner is the principle of the intersection of the bisector of the triangle angle: two tangents of the circle are made by a point outside the circle.

This point is bisected with the line at the center of the circle at the angle between the two tangents (principle: the distance from the point to the angle on the bisector is equal).

2. Outer center: It is the intersection point of the perpendicular bisector of the three sides of the triangle, that is, the circumscribed circle.

of the center of the circle. Centroid theorem: The perpendicular bisector of the three sides of a triangle intersects at a point. This point is called the outer center of the triangle.

3. Center: The triangle has only five kinds of center of gravity, vertical center, inner center, outer center, and side center.

If and only if the triangle is a regular triangle, the four centers are united into a center, which is called the center of the regular triangle.

4. Center of gravity: The center of gravity is the intersection of the three sides of the triangle.

5. Side center: One of the inner angle bisectors of the triangle intersects with the outer angle bisector of the other two angles, and the point is the side center of the triangle. The distance from the center to the three sides of the triangle is equal.

The triangle has three circumscribed circles and three circumcentricities. The center must be outside the triangle. Right-angled triangle.

The radius of the circumscribed circle on the hypotenuse is equal to half the circumference of the triangle.

The midpoint on the hypotenuse of a right triangle is equal to half of the hypotenuse, the midpoint of the hypotenuse is connected, and the triangle formed by its corresponding right angle is two isosceles, and the midpoint of the hypotenuse of the triangular row and several sides make a parallel line to form two triangles, small triangles, and this big triangle is similar, triangle.

Definition: A point that divides a line segment into two equal line segments.

Special Properties:In addition to having the properties of a general triangle, a right triangle has some special properties:

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.

3. In a right-angled triangle, the middle line on the hypotenuse is equal to half of the hypotenuse (that is, the outer center of the right-angled triangle is located at the midpoint of the hypotenuse, and the radius of the circumscribed circle r=c 2). This property is known as the hypotenuse midline theorem of a right triangle.

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.

Question 1: How to find the midpoint of the triangle accurately? The most important thing in learning mathematics is to understand the definition, and if you do, it is basically not difficult.

For example, in your question, find the middle point. You have to know what a midpoint is.

Midpoint: In a triangle, the line segment that connects a vertex to the midpoint of the opposite edge is called the midline of the triangle. Any triangular state has three middle lines, and these three middle lines are all inside the triangle and are intersected at one point.

In the end, you have to do it yourself, otherwise it will not be in the future, and it will become **Question 2: What is the connection line between the midpoints on both sides of the triangle called the median line of this triangle Median line question 3: What is the line segment connecting the midpoints on both sides of the triangle called the median line of the triangle.

The median line of the triangle is parallel to the third side and is equal to half the length of the third side.

There is also a median line: the median line of the trapezoid.

Definition: The line segment connecting the midpoints of the two waists of the trapezoid is called the median line of the trapezoid.

According to the question, the number of such ascending triangles is: 2n + 1 = 2 100 + 1 = 201, so the answer is: 201.

The relationship between the corners of triangles, test center comments: This question mainly examines the number of triangles determined by using the number of points in the plane, and the value obtained when taking a relatively small value according to n, finding out the law, masking and reusing the law to solve the problem.

The dots in the triangle, called the "heart" of the triangle, are divided into the inner, outer, centric, and perpendicular centers.

The perpendicular bisector of the three sides of a triangle intersects at a point, which is the outer center of the triangle, the outer center of an acute triangle is inside the triangle, the outer center of a right triangle is at the midpoint of the hypotenuse, and the outer center of an obtuse triangle is on the outside of the triangle.

The bisector of the three corners of the triangle intersects at one point, which is the heart of the triangle. The heart is inside the triangle.

The three midlines of the triangle intersect at one point, which is the center of gravity of the triangle, and the center of gravity is inside the triangle.

The three highs of the triangle intersect at one point, which is the vertical center of the triangle. The vertical center of an acute triangle is inside the triangle, the vertical center of a right triangle is at the vertex of the right angle, and the vertical center of an obtuse triangle is on the outside of the triangle.