Question

如圖1-4-10,在Rt△ABC中,∠BAC=90°,AD是高,且AB =2AC,求證:5AD =2BC.

圖1-4-10

Answer 1

思路分析:本題關鍵是把所求結論“5AD =2BC”與已知條件“AB =2AC”進行聯系,而聯系兩者的根本是射影定理.

證明:設AC =x,則AB =2x,?

由勾股定理得,?

在Rt△ABC中,∵AD⊥BC,?

∴AC²=CD·CB,  = = =.?

∴AD²=BD·CD =.?

∴.?

∴= =,即5AD =2BC.