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Question
In the given figure, if line AB || line CF and line BC || line ED then prove that ∠ABC = ∠FDE.
Solution
Let us mark the points M and N on line BC and point G on line ED.
Since line AB || line PF (or line CF) and line MN is their transversal,
∠PCN = ∠ABC ...(Corresponding angles)...(1)
Since line MN || line EG and line PF is their transversal, then
∠PCN = ∠CDG ...(Corresponding angles)...(2)
Since EG and PF are straight lines intersecting at D, then
∠CDG = ∠FDE ...(Vertically opposite angles) ...(3)
∴ from (2) and (3), we get
∠PCN = ∠FDE ...(4)
∴ from (1) and (4), we get
∠ABC = ∠FDE
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