1.

In the given figure, if line AB || line CF and line BC || line ED then prove that ∠ABC = ∠FDE.

Answer»

Given: line AB || line CF and line BC || line ED 

To prove: ∠ABC = ∠FDE

Proof: 

line AB || line PF and line BC is their transversal. 

∴ ∠ABC = ∠BCD ….(i) [Alternate angles] line BC || line ED and line CD is their transversal. 

∴ ∠BCD = ∠FDE ….(ii) [Corresponding angles] 

∴ ∠ABC = ∠FDE [From (i) and (ii)].



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