Answers

  • Brainly User
2014-09-18T12:24:36+05:30
As per figure, in triangles BGE and BDC, GE and DC are parallel, hence angle BGE = angle BDC and angle BEG = angle BCD, hence triangles BGE and BDC are similar. 
(1) GE/DC = BE/BC = 3/7 [ BE : EC = 3 : 4 (given), ==> BC =BE+EC = 7] 
    OR GE = (3/7)xDC = 2 x (3/7) x AB as DC = 2xAB (Given).
     OR GE = (6/7)xAB
(2) DG/DB = CE/CB = 4/7

(3) In triangles DFG and DAB, FG is parallel to AB. Hence triangles DFG and DAB are similar. [For similar reasons as for triangles BGE and BDC]

Therefore FG/AB = DG/DB = 4/7 [from (2) above]
                 OR FG = (4/7)xAB 

Hence EF =  GE + FG = (6/7)xAB + (4/7)xAB = (10/7)xAB
==> 7EF = 10AB  
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