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-side、side-side-side。這股熱潮，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，P是AB的中點，Q是BC的中點，R是CD的中點，S是DA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)