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Question
Use the information in the given figure to prove:
- AB = FE
- BD = CF
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Solution
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
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