Question

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

[Hint: Produce DE to intersect BC at P (say)].

Answer 1

According to the question:

Given: Producing DE to intersect BC at P.

EF || BC and DP is the transversal,

∠DEF = ∠DPC   ...(i) [Corresponding ∠s]

See the above figure, AB || DP and BC is the transversal,

∠DPC = ∠ABC  ...(ii) [Corresponding ∠s]

Now, from equation (i) and (ii), we get:

∠ABC = ∠DEF

Hence proved.