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

Question:

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

 

Solution:

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

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