Question

l have attached a picture.
In that figure , BA || DF and CA || EG and BD=EC. Prove that
1. BG=DF
2. EG=CF

Answer 1

in ∆ABC,
BD=EC(given) ...(i)
therefore, BD+DE=EC+DE
thus,BE=DC

in ∆ BEG & ∆ DFC
<GBE= <FDC (BA||DF)
BE=EC( from (i))
<GEB=<FCD(CA||EG)

therefore ∆BEG & ∆CDF are congruent to each other .

thus,
BG=DF(cpct*)
EF=CF(cpct)

*corresponding part of a congruent triangle