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

1.	In the figure, if EF \|\| CD. Prove that AB \|\| CD.
Answer» 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.

Answer»

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.

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