The midline theorem, also known as the center of gravity theorem, is a theorem of Euclidean geometry, which expresses the relationship between the three sides of a triangle and the length of the midline. The content of the theorem is that the sum of the squares of the opposite sides of the center line of a triangle is equal to twice the sum of the square of the half bottom plus the square of this center line. For any triangle, if I is the midpoint of BC and AI is the midline, there is the following relationship: AB square +AC square =2*BI square +2*AI square.
The three median lines of any triangle divide the triangle into six parts with equal area, and the median line divides the triangle into two parts with equal area. Besides, any other straight line passing through the midpoint will not divide the triangle into two parts with equal area. In a right triangle, the center line corresponding to the right side is half of the hypotenuse.
The midline of a triangle is a line segment connecting the vertex of the triangle with the midpoint of its opposite side. Each triangle has three median lines, all of which are inside the triangle. In a triangle, the intersection of three midlines is the center of gravity of the triangle. The three median lines of a triangle intersect at a point, which is located at two-thirds of each median line.
Application of midline property of triangle;
The midline theorem of triangle can be used to calculate the area of triangle. Suppose that the three sides of a triangle are A, B and C, and their corresponding heights are H, K and M, where m is the length of the center line of the triangle. According to the midline theorem, M divides C into two halves, and the length of each half is c/2, which is brought into the formula.
According to the calculation, 2S = cm. S represents the area, 2S is twice the area, cm is the product of the midline length m and c, and the area of a triangle can be expressed as: S = cm/2. When calculating the area of a triangle, using the midline theorem can avoid using such a complicated formula as sine theorem, which is very convenient in practical application.
The midline theorem can also be used to calculate the perimeter of a triangle. Assuming that the midline length of a triangle is m, n and p respectively, according to the midline theorem, their corresponding three sides are 2√(b? + c？ )/2、2√(a？ + c？ ) /2 and 2√(a? + b？ ) /2, where A, B and C are three sides of a triangle. Add up these side lengths to get the perimeter l of the triangle.