Question

In the given figure, BA || ED and BC || EF. Show that ∠ABC = ∠DEF.

Answer 1

It is given that, BA || ED and BC || EF.

Construction: Extend DE such that it intersects BC at J. Also, extend FE such that it intersects AB at H.



Now, BA || JD and BC is a transversal.

∴ ∠ABC = ∠DJC .....(1) (Pair of corresponding angles)

Also, BC || HF and DJ is a transversal.

∴ ∠DJC = ∠DEF .....(2) (Pair of corresponding angles)

From (1) and (2), we have

∠ABC = ∠DEF