91Ó°ÊÓ

The given diagram is:

It is being given that$\stackrel{¯}{XY}$ bisects$∠RXS$ and $∠RYS$.

As,$\stackrel{¯}{XY}$ bisects $∠RXS$.

Therefore, by using the definition of angle bisector it can be said that$∠RXYâ‰\dots ∠SXY$ .

As,$\stackrel{¯}{XY}$ bisects$∠RYS$ .

Therefore, by using the definition of angle bisector it can be said that .

$∠RYXâ‰\dots ∠SYX$

In the triangles$â–³RXY$ and $â–³SXY$, the side that is common is$XY$ .

Therefore,$\stackrel{¯}{XY}â‰\dots \stackrel{¯}{XY}$by using the reflexive property.

In the triangles $â–³RXY$ and $â–³SXY$, it can be noticed that$∠RYXâ‰\dots ∠SYX$, $\stackrel{¯}{XY}â‰\dots \stackrel{¯}{XY}$and$∠RXYâ‰\dots ∠SXY$.

Therefore, the triangles $â–³RXY$and $â–³SXY$are the congruent triangles by using the ASA postulate.

Yes, it can be deduced from the given information that$â–³RXYâ‰\dots â–³SXY$.

The postulate that can be used is ASA postulate.