91Ó°ÊÓ

If two angles of a triangle are congruent, then the sides opposite to those angles are congruent.

From the given figure it can be observed that$\stackrel{¯}{TR}$ is opposite to$∠S$ and$\stackrel{¯}{RS}$ is opposite to$∠T$.

As $∠Sâ‰\dots ∠T$, $\stackrel{¯}{TR}â‰\dots \stackrel{¯}{RS}$.

If two parallel lines are intersected by a transversal then the angles made by transversal with respect to lines are congruent and are called alternate angles.

As,$\stackrel{¯}{ST}\left|\right|\stackrel{¯}{QP}$ and$∠Tâ‰\dots ∠P;∠Qâ‰\dots ∠S$.

If$∠Aâ‰\dots ∠B$ and$∠Bâ‰\dots ∠C$ then $∠Aâ‰\dots ∠C$.

Since, $∠Pâ‰\dots ∠T$, $∠Tâ‰\dots ∠S$and $∠Sâ‰\dots ∠Q$implies that $∠Pâ‰\dots ∠Q$.

If two angles of a triangle are congruent, then the sides opposite to those angles are congruent.

From the given figure it can be observed that $\stackrel{¯}{QR}$is opposite to $∠P$and $\stackrel{¯}{PR}$is opposite to $∠Q$.

As $∠Pâ‰\dots ∠Q$, $\stackrel{¯}{PR}â‰\dots \stackrel{¯}{QR}$.

Write a two-column proof based on above explanation.

Therefore, only (1) and (2) statements are true.