在△ABC中,点P为BC中点,延长AB到D使BD=AC,延长AC到E使CE=AB,连接DE.连接DE,若角BAC=60度求BE与AP的关系,

Question

在△ABC中,点P为BC中点,延长AB到D使BD=AC,延长AC到E使CE=AB,连接DE.连接DE,若角BAC=60度求BE与AP的关系,

Answer 1

延长AP,取PF＝AP∵AB＝CE,AC＝BD,AD＝AB+BD,AE＝AC+CE∴AD＝AE∵∠BAC＝60∴等边△ADE∴∠ADE＝∠AED＝60∵P是BC中点∴BP＝CP∵AP＝PF∴平行四边形ABFC∴CF∥AD,CF＝AB∴∠ECF＝∠BAC＝60,CF＝CE∴等边△CEF∴∠CEF...