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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:

$\Delta DCB \sim \Delta HGE$

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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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