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CD and GH are respectively the bisectors of angle ACB and angle EGF such that D and H lie on sides AB and FE of triangle ABC and triangle EFG respectively. If Delta ABC is similar to Delta FEG, show that: (question 3)

Q10 (3)   CD and GH are respectively the bisectors of \angle ABC \: \:and \: \: \angle EGF such that D and H lie on sides AB and FE of \Delta ABC \: \:and \: \: \Delta EGF respectively. If \Delta ABC\sim \Delta EGF, show that: 

             \Delta DCA \sim \Delta HGF

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To prove : \Delta DCA \sim \Delta HGF

Given : \Delta ABC \sim \Delta EGF

In \Delta DCA \, \, \, and\, \, \Delta HGF,

\therefore \angle ACD=\angle FGH   ( CD and GH are bisectors of equal angles)

   \angle A=\angle F           ( \Delta ABC \sim \Delta EGF)

    \Delta DCA \sim \Delta HGF     ( By AA criterion )

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