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CD and GH are respectively the bisectors of angle ACB and angle EGF such that D and H liye on sides AB and FE of triangle ABC and triangle EFG respectively. If triangle ABC similar to triangle FEG,show that: CD/GH =AC/FG

Posted by Gunja Gupta 5 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 3 months ago

It is given that ΔABC ∼ ΔFEG.

∴ ∠A = ∠F, ∠B = ∠E, and ∠ACB = ∠FGE

∠ACB = ∠FGE

∴ ∠ACD = ∠FGH (Angle bisector)

And, ∠DCB = ∠HGE (Angle bisector)

In ΔACD and ΔFGH,

∠A = ∠F (Proved above)

∠ACD = ∠FGH (Proved above)

∴ ΔACD ∼ ΔFGH (By AA similarity criterion)

=>(CD)/(GH) = (AC)/(FG)

1Thank You

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