13 (c) in the figure, BA is parallel to DF and CA is parallel to EG and BD = EC - Maths -

Question

13 (c) in the figure, BA is parallel to DF and CA is parallel to EG
and BD = EC prove that
(i)BG=DF
(ii)EG=CF

Lovina Kansal · Accepted Answer

Dear student
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Since BD=EC⇒BD+DE=DE+EC⇒BE=DC    
(1)Since GB∥DF and GE is their trannsversal
⇒∠BGE=∠GOF    [alternate interior angle]    
(2)and FC∥EG and FD is their transversalSo, ∠DFC=∠GOF     [alternate interior angle]    
(3)So, from (2) and (3), we have∠BGE=∠DFC     
(4)Since GB∥DF and BC is their trannsversal
∠GBE=∠FDC     [corresponding angles]Now, in △GBE and △FDC∠BGE=∠DFC∠GBE=∠FDCBE=DCSo, △GBE≅△FDC    [By AAS]⇒BG=DF and EG=CF    [CPCT

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13.(c) in the figure, BA is parallel to DF and CA is parallel to EG and BD = EC. prove that (i)BG=DF (ii)EG=CF

13.(c) in the figure, BA is parallel to DF and CA is parallel to EG and BD = EC. prove that
(i)BG=DF
(ii)EG=CF