Question 10 (i) CD and GH are respectively the bisectors of ∠ACBand∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC∼ΔFEG, Show that (i)CDGH=ACFG
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Solution
(i) It is given that ΔABC∼ΔFEG. ∴∠A=∠F,∠B=∠E,and∠ACB=∠FGE ∴∠ACD=∠FGH (Angle bisector) And, ∠DCB=∠HGE (Angle bisector)
In ΔACDandΔFGH, ∠A=∠F ∠ACD=∠FGH ∴ΔACD∼ΔFGH (By AAA similarity criterion) ⇒CDGH=ACFG