Question

Question 10 (iii)
CD and GH are respectively the bisectors of $angleACB$ and $\angle EGF$ such that D and H lie on sides AB and FE of $\Delta ABC$ and $\Delta EFG$ respectively. If $\Delta ABC\sim \Delta FEG$, Show that
$\left(iii\right)\Delta DCA\sim \Delta HGF$

Answer 1

(iii) In $\Delta DCAand\Delta HGF$,
$\angle ACD=\angle FGH$ (CD and GH are bisectors of $\angle ACB$ and $\angle EGF$ ,also it is given that$\Delta ABC\sim \Delta FEG$)
$\angle A=\angle F$ ( $\Delta ABC\sim \Delta FEG$)
$\therefore \Delta DCA\sim \Delta HGF$ (By AAA similarity criterion)