Q

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:

$\Delta DCA \sim \Delta HGF$

Views

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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