91Ó°ÊÓ

The labelled diagram is:

It is being given that $∠2â‰\dots ∠3$.

Therefore, $∠BGHâ‰\dots ∠CHG$.

From the given diagram it can be noticed that the angles $∠BGH$and$∠CHG$ are alternate interior angles.

If the two lines are parallel and there is a transversal then the alternate interior angles are congruent.

Therefore, as alternate interior angles$∠BGH$ and$∠CHG$ are congruent.

Therefore, the lines AB and CD are parallel.

Therefore, it can be deduced that the lines AB and CD are parallel.

The labelled diagram is:

It is being given that$∠2â‰\dots ∠3$.

From the given diagram it can be noticed that the angles$∠AGE$ and$∠BGH$ are the vertically opposite angles.

Therefore, $∠AGEâ‰\dots ∠BGH$.

Therefore, it can be obtained that:

$\begin{array}{c}∠AGEâ‰\dots ∠BGH\\ ∠1â‰\dots ∠2\end{array}$

As,$∠1â‰\dots ∠2$ and $∠2â‰\dots ∠3$, therefore by using the transitive property of congruence it can be said that$∠1â‰\dots ∠3$

As, $∠1â‰\dots ∠3$, therefore $∠AGEâ‰\dots ∠CHG$.

From the figure it can be noticed that the angles$∠AGE$ and$∠CHG$ are corresponding angles.

If the two lines are parallel and there is a transversal then the corresponding angles are congruent.

Therefore, as corresponding angles $∠AGE$and $∠CHG$are congruent.

Therefore, the lines AB and CD are parallel.

Hence proved.