Question

In the figure, if EF || CD. Prove that AB || CD.

Answer 1

We are given that EF || CD

EF || CD

∠FEC + ∠ECD = 180° (Sum of the interior angles on the same side of a transversal is 180°)

⇒ 125° = ∠ECD = 180°

⇒ ∠ECD = 180° – 125° = 55°

⇒ ∠BCD = ∠BCE + ∠ECD 

= 25° + 25° = 80°

∠ABC = ∠BCD = 80°

These are alternate interior angles and they are equal.

Hence, AB || CD.