Question

如圖，等邊三角形OAB繞點(diǎn)O順時(shí)針旋轉(zhuǎn)120°后得到△ODE，那么點(diǎn)B的對(duì)應(yīng)點(diǎn)是________OA的對(duì)應(yīng)線________，∠B的對(duì)應(yīng)角________，旋轉(zhuǎn)角是________和________，都等于________．

Answer 1

點(diǎn)E    OD    ∠E    ∠BOE    ∠AOD    120°
分析：①對(duì)應(yīng)點(diǎn)到旋轉(zhuǎn)中心的距離相等；②對(duì)應(yīng)點(diǎn)與旋轉(zhuǎn)中心所連線段的夾角等于旋轉(zhuǎn)角．
解答：如圖，∵等邊三角形OAB繞點(diǎn)O順時(shí)針旋轉(zhuǎn)120°后得到△ODE，
∴△OAB≌△ODE，∠AOD=∠BOE=120°，
∴OB=OE，OA=OD，∠B=∠E，
∴點(diǎn)B的對(duì)應(yīng)點(diǎn)是點(diǎn)E，OA的對(duì)應(yīng)線OD，∠B的對(duì)應(yīng)角∠E，旋轉(zhuǎn)角是∠BOE和∠AOD，都等于120°．
故答案是：點(diǎn)E，OD，∠E，∠BOE和∠AOD，120°．
點(diǎn)評(píng)：此題考查了旋轉(zhuǎn)的性質(zhì)：旋轉(zhuǎn)前后的兩個(gè)圖形全等，對(duì)應(yīng)點(diǎn)與旋轉(zhuǎn)中心的連線段的夾角等于旋轉(zhuǎn)角，對(duì)應(yīng)點(diǎn)到旋轉(zhuǎn)中心的距離相等．