求作四边形的重心(高一)

• 作 者: 翟羽佳
• 机 构: 江苏省泰州市兴化中学高二(2)班 225700
• 出 处: 数理天地(高中版)
• 发表日期: 2003年05期
• 关键词: 辅助线 二等分 法要 自形

求作四边形的重心,一般作法是沿四边形的一条对角线将四边形分成两个三角形,作出它们的重心连线.同理,沿另一条对角线分割,可以作出另一条重心连线,这两条重心连线的交点就是四边形的重心.这种作法要画12条辅助线,图形比较繁杂.我们知道,三角形的重心是两条面积二等分线的交点.依照这个原理,我们可以将四边形的面积两次二等分,两条二等分线的交点即为四边形的重心.作法如下:

To achieve the center of gravity of the quadrilateral, it is common practice to divide the quadrilateral into two triangles along a diagonal of the quadrilateral, making their center of gravity connections. Similarly, dividing along another diagonal line can make another center of gravity connection. The intersection of the two centers of gravity is the center of gravity of the quadrilateral. This approach draws 12 auxiliary lines and the graphics are more complicated. We know that the center of gravity of the triangle is the intersection of the two area bisectors. According to this principle, we can The area of ​​the quadrilateral is divided into two equal parts. The intersection of the two bisecting lines is the quadrilateral center of gravity. The method is as follows: