Question

Use the information in the given figure to prove ;
AB = FE

Answer 1

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

$$AC = ED$$ (given )

$$ \angle ACB = \angle EFD $$ (given)

$$ \Delta ACB \cong \Delta EFD $$ ( AAS congruence criterion )
$$\Rightarrow AB = FE $$ (cpct)