Question

Use the information in the given figure to prove:

1. AB = FE
2. BD = CF 

Answer 1

ln ΔABC and ΔEFD,

AB II EF

⇒ ∠ABC = ∠EFD         ...(alternate angles)

AC = ED                              ...(given)

∠ACB = ∠EDF                    ...(given)

∴ ΔABC ≅ ΔEFD               ...(AAS congruence criterion)

⇒ AB = FE                           ...(cpct)

and BC = DF                        ...(cpct)

⇒ BD + DC = CF + DC       ...(B-D-C-F)

⇒ BD = CF