Question

CD and GH are respectively the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC ∼ ΔFEG, Show that: (i) CD/GH = AC/FG (ii) ΔDCB ∼ ΔHGE (iii) ΔDCA ∼ ΔHGF

Answer 1

If you satisfy with this answer please add in Brainlliest.

Answer 2

Given : GH and CD are angle bisectors.

To prove : ∆DCA~∆HGF, CD/GH = AC/FG and ∆DCB ~ ∆HGE.

Proof : By similarity criteria we know that ∠A = ∠F, ∠B = ∠E and ∠C = ∠G.

→ ∠C = ∠G

→ ½ ∠C = ½ ∠G

→ ∠1 = ∠3 and ∠2 = ∠4 __(1)

(i) When ∠A = ∠F and ∠2 = ∠4 then by AA similarity criteria ∆DCA ~ ∆HGF.

(ii) Due to above proving, CD/GH = AC/FG.

(iii) When ∠B = ∠E and ∠1 = ∠3 then by AA similarity criteria, ∆DCB ~ ∆HGE.

Q.E.D