In each of the following figures, two lines AB and CD are cut by a transversal EF. In each case, find whether AB || CD or not. Give reasons in support of your answer.

(i)

(ii)

(iii)

(iv)

(v)

(i)

In the given figure,

The angle vertically opposite to 40° is 40°.

Now, consider the pair of co-interior angles: 130° and 40°.

Sum = 130° + 40° = 170°

Since the sum of co-interior angles is not 180°.

AB and CD are not parallel.

(ii)

At the first intersection, the interior angle adjacent to 100° is 180° - 100° = 80° (Linear pair).

This 80° angle and the given 80° angle at the second intersection are corresponding angles.

Since 80° = 80°, the corresponding angles are equal.

AB and CD are parallel.

(iii)

The sum of angle adjacent to 120° and 120° is 180° because they form linear pair.

So,

Adjacent angle = 180° - 120° = 60°

This 60° angle and the given 60° angle are exterior alternate angles.

Since 60° = 60°, the external alternate angles are equal.

AB and CD are parallel.

(iv)

From the figure we have,

AD is a transversal

∠BAD = 50° and ∠ADC = 40°

These form a pair of interior alternate angles.

But 50° $\neq$ 40°

Since alternate angles are not equal,

AB and CD are not parallel.

(v)

The angles 75° and 100° are a pair of co-interior angles.

Co-interior angles are supplementary.

Sum = 75° + 100° = 175°

Since the sum of co-interior angles is not 180°,

AB and CD are not parallel.