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中线定理:在△ABC中,AD为BC边上的中线,则 AB~2+AC~2=2(AD~2+CD~2) (1) 题目:从等轴双曲线的中心到其上任一点M的距离是两焦点到M点的距离的比例中项。分析:设等轴双曲线方程为x~2-y~2=a~2,其图象如左图,假设M点在图象的右支上,焦点坐标为F(c,0)F＇(-c,0),一般传统的解法是:设M点坐标为(x,y),根据两点间距离公式求出|MO|、|MF|、|MF＇|,然后利用已知条件进行变换,最后求出结果,其过程较为繁杂。但是利用中线定理,则可以避免繁冗的计算,其中最突出的优点是不需设M点坐标;
Midline theorem: In △ABC, AD is the midline on the BC side, then AB~2+AC~2=2(AD~2+CD~2) (1) Problem: From the center of the isochronal hyperbola to its center The distance of a point M is the proportion of the distance between two focal points to M points. Analysis: Let the isometric hyperbolic equation be x~2-y~2=a~2. The image is shown on the left. Assume that the M point is on the right branch of the image and the focal coordinate is F(c, 0)F’. (-c, 0), the general traditional solution is: set the coordinates of the M point to (x, y), find |MO|, |MF|, |MF’| based on the distance between the two points, and then use the known condition Transforming and finally finding the result is a complicated process. However, using the midline theorem can avoid tedious calculations. The most prominent advantage is that there is no need to set the coordinates of M points;