tfvnjy

In the figure, DBCF , DACD and DEFD are equilateral triangles.Show that AB = EF

芊羽

hint: try to prove ΔABC and ΔAED are congruent.

tfvnjy

有冇人可以prove俾我睇?

桃子

I think the given conditions may be insufficient.

kittrash

hint: try to prove ΔABC and ΔAED are congruent.

sorry, ΔABC and ΔAED may not be  congruent, but the result AB = EF can still hold

kittrash

sorry all , i may get wrong in previous post ~~

must be congruent ~~

kittrash

possible one ~~

first prove  ΔABC and ΔDFC are congruent
then prove  ΔDEA  and ΔDFC are congruent

桃子

It's a hard question.

BC=FC (property of equil. Δ)
AC=DC (property of equil. Δ)
angle BCF=angle ACD (property of equil. Δ)
angle BCA+angle ACF=angle ACF+angle FCD
angle BCA=angle FCD
ΔABC is congruent to ΔDFC. (SAS)

AB=DF (corr. sides, congruent Δs)
DF=EF (property of equil. Δ)
AB=EF

tfvnjy

thx a lot~