Question

將矩形紙片ABCD如圖那樣折疊，使頂點(diǎn)B與頂點(diǎn)D重合，折痕為EF．若AB=

3

，AD=3，則△DEF的周長為______．

Answer 1

連接BD交EF于H點(diǎn)．
∵AB=

3

，AD=3，∴∠ADB=30°．
∵AD∥BC，F(xiàn)B=FD，∴∠ADB=∠DBF=∠BDF=30°．
∴∠A'DE=∠ADB=30°，∠BDF=∠FDC=30°．
∴EH=EA'=EA，F(xiàn)H=FC．
∴△DEF的周長為DE+EH+HF+DF=2AD=6．