Question

Question 10 (ii)
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
$\left(ii\right)\Delta DCB\sim \Delta HGE$

Answer 1

(ii) In $\Delta DCBand\Delta HGE$,
$\angle DCB=\angle HGE$ (Halves of $\angle$BCA and $\angle$FGE)
$\angle B=\angle E$ (Because it is given that $\Delta ABC\sim \Delta FEG$)
$\therefore \Delta DCB\sim \Delta HGE$ (By AAA similarity criterion)