Outer center: the center of the circumscribed circle of a triangle is the intersection of the perpendicular lines of the three sides of the triangle. Inner center: the center of the inscribed circle of a triangle is the intersection of the bisectors of the three inner angles of the triangle. Center: The outer center and inner center of a regular polygon (such as an equilateral triangle) overlap with each other, also called the center, which is the rotation center of the regular polygon. Center of gravity: the intersection of the midlines of three sides of a triangle. Vertical center: the intersection of three heights of a triangle.

Triangle (triangle)

It is a closed figure composed of three line segments in the same plane but not on the same straight line, which has applications in mathematics and architecture. Ordinary triangles are divided into ordinary triangles according to their sides (three sides are unequal).

Isosceles triangle (isosceles triangle with unequal waist bottom and isosceles triangle with equal waist bottom, that is, equilateral triangle); According to the angle, there are right triangle, acute triangle and obtuse triangle, among which acute triangle and obtuse triangle are collectively called oblique triangle.

A closed figure composed of three line segments that are not on the same straight line is called a triangle. A figure surrounded by three straight lines on a plane or three arcs on a sphere is called a plane triangle; A figure surrounded by three arcs is called a spherical triangle, also known as a triangle. A closed geometry consisting of three line segments connected end to end is called a triangle. Triangle is the basic figure of geometric figure.

Divide by edge

1, equilateral triangle; An equilateral triangle is mathematically defined as a triangle with three unequal sides.

2, isosceles triangle; An isosceles triangle refers to a triangle with two equal sides, which are called the waist of the triangle. In an isosceles triangle, two equal sides are called waist and the other side is called bottom. The angle between the two waists is called the top angle, and the angle between the waist and the bottom edge is called the bottom angle.

The two base angles of an isosceles triangle are equal (abbreviated as "equilateral angles"). The bisector of the vertex, the midline of the bottom and the height of the bottom of an isosceles triangle coincide (referred to as "the three-line unity property of an isosceles triangle"). The bisectors of the two base angles of an isosceles triangle are equal (the median lines of the two waists are equal and the heights of the two waists are equal).

The median vertical line on the bottom of the isosceles triangle is equal to the distance between the two waists. The angle between the waist height and the bottom of an isosceles triangle is equal to half of the top angle. The sum of the distances from any point on the bottom of an isosceles triangle to two waists is equal to the height of one waist (proved by equal area method).

An isosceles triangle is an axisymmetric figure with only one axis of symmetry (when it is not an equilateral triangle). The line where the bisector of the top angle is located is its symmetry axis, and an equilateral triangle has three symmetry axes. The square of the waist in an isosceles triangle is equal to the square of the height plus half the square of the bottom.

The direct relationship between waist and height of isosceles triangle is that waist is greater than height. The indirect relationship is that the square of waist circumference is equal to the square of height plus half of the square of ass.

3. equilateral triangle. An equilateral triangle (also called a regular triangle) is a triangle with three equal sides and three equal internal angles, all of which are 60 degrees. This is an acute triangle. An equilateral triangle is also the most stable structure. An equilateral triangle is a special isosceles triangle, so it has all the properties of an isosceles triangle.