Question

初一数学，急

Answer 1

∵△ABC是等边三角形
∴∠ABC=∠ACB=60°
∵BD=CD
∠BDC=120°
∴∠DBC=∠DCB=30°
∴∠ABD=∠ACD=∠ABC+∠DBC=90°
将Rt△BDE逆时针旋转使BD与CD重合，得到Rt△CDE′
∴DE=DE′ ∠BDE=∠CDE′ BE=CE′
∵∠EDF=60°
∴∠BDE+∠CDF=120°-60°=60°
∴∠FDE′=∠CDF+∠CDE′=∠CDF+∠BDE=60°
∴∠EDF=∠FDE′
在△EDF和△FDE′中
∠EDF=∠FDE′
DF=DF
DE=DE′
∴△EDF≌△FDE′
∴EF=FE′
∴△AEF的周长
=AE+EF+AF
=AE+FE′+AF
=AE+FC+CE′+AF
=AE+BE+FC+AF
=AB+AC
=1+1
=2