Question

Use the information in the given figure to prove ;
BC = DF

Answer 1

In $$ \Delta ABC$$ and $$\Delta EFD $$
$$AB || EF \Rightarrow \angle ABC = \angle EFD $$ (alternate angles )

$$AC = ED $$ (given )

$$ \angle ABC = \angle EFD $$ ( alternate angles )

$$ \Delta ACB \cong \Delta EFD $$ ( AAS congruence criterion )

And $$BC = DF$$ (cpct)

Adding $$DC$$ we get:

$$\Rightarrow BD + DC = CF + DC $$
$$\Rightarrow BC = DF $$