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CD and GH are respectively the bisector...

CD and GH are respectively the bisectors of `/_A C B`and `/_E G F`such that D and H lie on sides AB and FE of `DeltaA B C\ and\ DeltaE F G`respectively. If`DeltaA B C DeltaF E G`, show that:
(i) `(C D)/(G H)=(A G)/(F G)`
(ii) `∆ DCB ~ ∆ HGE`
(iii) `∆ DCA ~ ∆ HGF`

Text Solution

Verified by Experts

In △ABC and △FEG,
`△ABC∼FEG
∴ `/_ACB`= `/_EGF`
(Corresponding angles of similar triangles)
Since, DC and GH are bisectors of `/_ACB` and `/_EGH` respectively.
∴ `/_ACB=2` `/_ACD=2``/_BCD`
And `/_EGF=2` `/_FGH=2` `/_HGE`
∴ `/_ACD=` `/_FGH` and `/_DCB=` `/_HGE` ...................(1)
Also `/_A=` `/_F` and `/_B=` `/_E` ...............(2)
...
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