1. What is the center line of the triangle?
In a triangle, the line segment formed by connecting the midpoints of each side is called the midline. A triangle has three median lines, which connect the midpoints of the three vertices respectively.
2. The expression of triangle midline theorem:
The midline theorem of triangle shows that the three midlines of triangle are equal in length, and the length is equal to half of the side length.
3. Derivation of centerline length:
Through geometric derivation, the specific formula for calculating the length of the triangle midline can be obtained. Suppose that the three vertices of a triangle are A, B and C, and the three sides are A, B and C respectively. According to the definition of the midline, the length of the line segment connecting AB is equal to half of AC, BC is equal to half of AB, and AC is equal to half of BC.
4. Application example:
For example, we know that the lengths of the three sides of a triangle are 6cm, 8cm and 10cm respectively, so we can calculate the lengths of the three midlines according to the triangle midline theorem. The length of the midline connecting AB is equal to half of AC, that is, 4 cm; The length of the midline connecting BC is equal to half of AB, that is, 3 cm; The length of the center line connecting AC is equal to half of BC, that is, 5cm.
Expand knowledge:
According to the geometric properties of triangles, the midline theorem of triangles is deduced. According to the midline theorem of triangle, if the side length of triangle is known, the lengths of three midlines can be obtained by calculating half of the side length. The triangle midline theorem has application in finding the triangle area and judging the triangle type.
Summary:
The formula of triangle midline theorem shows that the three midlines of a triangle are equal in length, and the length is equal to half of the side length. Using this theorem, we can calculate the length of the center line of a triangle, which can be applied to geometric and mathematical problems. Through deduction and practical application examples, we can better understand and apply the triangle midline theorem.