Question

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

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