DE is parallel to OB, EF Is parallel to BC prove that DF parallel OC Share with your friends Share 6 Neha Sethi answered this Dear student In △ABO, we haveDE∥OB∴By Basic proportionality Theorem, we haveAEEB=ADDO ...(1)In △ABC, we haveEF∥BC∴By Basic proportionality Theorem, we haveAEEB=AFFC ...(2)From (1) and (2), we haveADDO=AFFC⇒DF∥OC By the converse of Basic proportionality Theorem Regards 9 View Full Answer Aakash Anand answered this We have given 1. D E is parallel to O B 2. E F is parallel to BC To prove:- D F is parallel to O C Proof:- In the given question we produce E D to H and B O to G and produce A O to intersect B C at M. We also produce F D to N and CO to P. Now, angle H D F = angle M D E (vertically opposite angles) angle G O C = angle P O B Now, since angle M D E = angle P O B (Since E D is parallel to B O and A M is transversal) Hence angle H D F = angle G O C Now, angle A D H = angle DOG Now, 180-(angle A D H+angle H D F)=180-(angle G O C+angle G O D ) angle M D F=angle M O C 1 D F is parallel to O C (if we consider AM a transversal then from 1) Thus proved. 2