CD and GH are respectively the bisectorsof ∠ ACB and ∠ EGF in such a way that D and H lieon sides AB and FE of Δ ABC and Δ EFGrespectively.

: It is given that ΔABC  ΔFEG

∠A = ∠F, ∠B = ∠E, and ∠ACB = ∠FGE

∠ACB = ∠FGE

∠ACD = ∠FGH (Angle bisector)

And, ∠DCB = ∠HGE (Angle bisector)

(i)          In ΔACD and ΔFGH,

∠A = ∠F (Proved above)

∠ACD = ∠FGH (Proved above)

∴ΔACD~ ΔFGH (By AA similarity criterion)

 (Corresponding sides of similar triangles are proportional)

(ii)         In triangle DCB and HGE

∠DCB = ∠HGE     (Proved above)

∠B = ∠E     (Proved above)

Therefore,

ΔDCB~ ΔHGE (By AA similarity criterion)

(iii)       In ΔDCA and ΔHGF,

∠ACD = ∠FGH (Proved above)

∠A = ∠F (Proved above)

ΔDCA ~ΔHGF (By AA similarity)