Question

Which pair of lines in the given figure are parallel? Given reasons.

Answer 1

The figure is given as follows:

We haveand.

Clearly,

.

These are the pair of consecutive interior angles.

Theorem states: If a transversal intersects two lines in such a way that a pair of consecutive interior angles is supplementary, then the two lines are parallel.

Thus, .

Similarly, we have and.

Clearly,

.

These are the pair of consecutive interior angles.

Theorem states: If a transversal intersects two lines in such a way that a pair of consecutive interior angles is supplementary, then the two lines are parallel.

Thus,.

Hence the lines which are parallel are as follows:

and .