In the figure (3) given below, BA || DF and CA || EG and BD = EC. Prove that

(i) BG = DF

(ii) EG = CF.

Given,

BD = EC

BD + DE = DE + EC

BE = DC.

Considering △BGE and △DFC,

∠GBE = ∠FDC (Corresponding angles)

∠GEB = ∠FCD (Corresponding angles)

BE = DC (Proved).

∴ △BGE ≅ △DFC by ASA axiom..

We know that corresponding parts of congruent triangles are equal.

∴ BG = DF.

Hence, proved that BG = DF.

(ii) We know,

△BGE ≅ △DFC.

We know that corresponding parts of congruent triangles are equal.

∴ EG = CF.

Hence, proved that EG = CF.