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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 triangle ABC is similar to triangle FEG, show that: (question 2 )

Q 10 (2)  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 DCB \sim \Delta HGE

Answers (1)
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To prove : \Delta DCB \sim \Delta HGE

Given : \Delta ABC \sim \Delta EGF

In \Delta DCB \,\, \, and\, \, \Delta HGE,

\therefore \angle DCB=\angle HGE   ( CD and GH are bisectors of equal angles)

   \angle B=\angle E           ( \Delta ABC \sim \Delta EGF)

    \Delta DCB \sim \Delta HGE     ( By AA criterion )

 

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