2016年4月29日 星期五

一道有趣的幾何學問題



近日,幾何學突然成為了網上熱潮,大家都愛上了side-angle-sideside-side-side。這熱潮,簡直比得上《美國隊長》。既然如此,史丹福也來分享一條頗為有趣的幾何學題目。(是前幾天表弟問我的)

ABCD是一個任意四邊形,PAB的中點,QBC的中點,RCD的中點,SDA的中點,試證明PQRS是一個平行四邊形(parallelogram)



答案:
Join AC.
S is the mid-point of DA, R is the mid-point of DC
Therefore AC = 2SR and AC // SR (Mid-point theorem)
P is the mid-point of BA, Q is the mid-point of BC
Therefore AC = 2PQ and AC // PQ (Mid-point theorem)
AC = 2SR = 2 PQ => SR = PQ
AC // SR // PQ => SR // PQ
Therefore PQRS is a parallelogram (opposite sides equal and parallel)

沒有留言:

張貼留言