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CD and GH are respectively the …

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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 4 years, 9 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 4 years, 9 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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