91Ó°ÊÓ

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

It is given that,$\stackrel{¯}{PQ}â‰\dots \stackrel{¯}{PR}$ and$\stackrel{¯}{TR}â‰\dots \stackrel{¯}{TS}$

Therefore,$∠Qâ‰\dots ∠PRQ$andwidth="96">∠TRS≅∠S

Angles formed due intersection of two lines are vertically opposite angles and they are equal in measures. From the figure it can be observed that $∠PRQ$and$∠TRS$ are vertically opposite angles. Therefore, $∠PRQâ‰\dots ∠TRS$.

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

Since, $∠Qâ‰\dots PRQ$, $∠PRQâ‰\dots ∠TRS$and $∠TRSâ‰\dots ∠S$implies that $∠Qâ‰\dots ∠S$.

If two lines are intersected by a transversal and alternate interior angles are congruent then the lines are parallel.

Therefore,$\stackrel{¯}{ST}\left|\right|\stackrel{¯}{QP}$and$∠Tâ‰\dots ∠P$.

Write a two-column proof based on above explanation.

Therefore, only (1) and (3) statements are true.