Question

In the given figure, if line AB || line CF and line BC || line ED

then prove that $\angle$ABC = $\angle$FDE.

Answer 1

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, then
∠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