E is an exterior point on diagonal AC of a parallelogram ABCD and DC produced meets BE at F - Maths - Triangles

Question

E is an exterior point on diagonal AC of a
parallelogram ABCD and DC produced meets BE at F If side BC
produced meets DE at G, prove that DB is parallel to
GF

Priyanka Kedia · Accepted Answer

Given that: ABCD be a parallelogram and E
is an exterior point on diagonal AC
To Prove: DB is parallel to GF
Construction: Join GF and DB
<img src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ana_qa_image_57b2eb39a3050%20png">

Proof:
In ΔABE,CF||AB            because, CD||ABBy basic proportionality theorem,EFFB=ECCA      
1Similarly, In ΔADE,CG||AD         because, BC||ADBy basic proportionality theorem,EGGD=ECCA      
2from 1 and 2,EFFB=EGGD⇒DB||GF  by converse of basic proportionality theoremHence Proved

E is an exterior point on diagonal AC of a parallelogram ABCD and DC produced meets BE at F. If side BC produced meets DE at G, prove that DB is parallel to GF

^{E is an exterior point on diagonal AC of a parallelogram ABCD and DC produced meets BE at F. If side BC produced meets DE at G, prove that DB is parallel to GF}