Question

如图,以三角形ABC的各边为边.在BC的同一侧作正三角形DBC,正三角形ABE,正三角形ACF.(1)说明四边形AEDF

Answer 1

在△ABC和△EBD中,

AB = EB ,∠ABC = ∠DBC+∠DBA = ∠EBA+∠DBA = ∠EBD ,BC = BD ,

所以,△ABC ≌ △EBD ,可得：AC = ED ,则有：AF = AC = DE .

同理可证：△ABC ≌ △FDC ,可得：AB = FD ,则有：AE = AB = DF .

由 AF = DE ,AE = DF ,可得：四边形AEDF是平行四边形.