Question

In the given figure, AE = DB, CB = EF and ∠ABC = ∠FED. Then, which of the following is true?
(a) ∆ABC ≅ ∆DEF
(b) ∆ABC ≅ ∆EFD
(c) ∆ABC ≅ ∆FED
(d) ∆ABC ≅ ∆EDF

Answer 1

(a) $△ABC\cong △DEF$

AE = DB ...(Given)
CB = EF ...(Given)

$AB=(AD-DB)=(AD-AE)andDE=(AD-AE)$
$$\begin{gathered} \mathrm{In}△\mathrm{ABC}\mathrm{and}△\mathrm{DEF},\mathrm{we}\mathrm{have}: \\ \mathrm{AB}=\mathrm{DE}\left(\mathrm{Proved}\right) \\ \mathrm{CB}=\mathrm{EF}...\left(\mathrm{Given}\right) \\ \angle \mathrm{ABC}=\angle \mathrm{FED}...\left(\mathrm{Given}\right) \\ △\mathrm{ABC}\cong △\mathrm{DEF}(\mathrm{SAS}\mathrm{criterion}) \end{gathered}$$