Question

如图,已知△ABC中,AD平分∠BAC,CD⊥AD,DE∥BA,求证:BC=2BE.

图1-1-13

Answer 1

思路解析:要证BC=2BE,即证E为BC的中点,联系已知条件DE∥AB,考虑平行线等分线段定理的推论,延长CD交AB于点F,只要证点D为FC的中点即可.

证明:延长CD交AB于点F,?

∵AD平分∠FAC,?

∴∠FAD=∠CAD.?

在△AFD和△ACD中,?

∵

∴△AFD≌△ACD.?

∴FD =CD.?

又∵DE∥AB,?

∴BE =EC,即BC =2BE.