one

theorem

Gravity center theorem: Three midlines of a triangle intersect at a point, which is the vertex.

The distance is twice the distance from the opposite midpoint. This point is called the center of gravity of the triangle.

Eccentricity theorem: the perpendicular lines of three sides of a triangle intersect at one point. This point is called the outer center of the triangle.

Vertical center theorem: three heights of a triangle intersect at one point. This point is called the center of the triangle.

Interior Theorem: The bisectors of three interior angles of a triangle intersect at one point. This point is called the heart of a triangle.

Proximity theorem: the bisector of the inner angle of a triangle intersects the bisector of the outer angle of the other two vertices at one point. This point is called the center of the triangle. A triangle has three side centers.

The center of gravity, outer center, vertical center, inner center and lateral center of a triangle are called the five centers of the triangle. Are all important connection points of the triangle.

The above conclusion was discovered as early as Euclid's time. In addition to sag theorems, Euclid collected them as important theorems in his Elements of Geometry. However, many studies on these special related points of triangles and many famous conclusions drawn from them later show that the omission of sag theorem is the negligence of the author of Geometry Elements.