Question
In the given figure, BA || ED and BC || EF. Show that $\angle\text{ABC}=\angle\text{DEF}.$
✓
Answer
Construction: Produce DE to meet BC at Z. 
Now, AB || DZ and BC is the transversal.$\Rightarrow\angle\text{ABC}=\angle\text{DZC}$ (corresponding angles) ….(i)
Also, EF || BC and DZ is the transversal.$\Rightarrow\angle\text{DZC}=\angle\text{DEF}$ (corresponding angles) ….(ii)
From (i) and (ii), we have$\angle\text{ABC}=\angle\text{DEF}$
Now, AB || DZ and BC is the transversal.$\Rightarrow\angle\text{ABC}=\angle\text{DZC}$ (corresponding angles) ….(i)Also, EF || BC and DZ is the transversal.$\Rightarrow\angle\text{DZC}=\angle\text{DEF}$ (corresponding angles) ….(ii)
From (i) and (ii), we have$\angle\text{ABC}=\angle\text{DEF}$
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