一、一组面积定理本文使用的记号“△PQR”表示三角形PQR,也表示它的面积.定理1(五点面积定理)设A、B和C、D是平面上任意两组点,另外有第五点O与A、B共线于l,则△OAC·△OBD=△OAD·△OBC①注:上式构成特征是:对于满足O、A、B共线而C、D为任意的这样五点,让OA、OB分别与C、D组合,成为①左端两个三角形顶 1. A set of area theorems The notation “ΔPQR” used in this paper denotes a triangle PQR, which also represents its area. Theorem 1 (five-point area theorem) Let A, B and C, D be any two sets of points in the plane, and The fifth point O is collinear with A and B at l, then ΔOAC·ΔOBD=ΔOAD·ΔOBC1 Note: The compositional features of the above equation are: For satisfying O, A, B collinear lines and C, D are arbitrary At five o’clock, OA and OB are combined with C and D, respectively, and they become 1 left triangle tops