91Ó°ÊÓ

The given diagram is:

It is being given that$∠2â‰\dots ∠3$and$∠1â‰\dots ∠4$.

As, $∠2â‰\dots ∠3$and $∠1â‰\dots ∠4$,therefore $∠2=∠3$and $∠1=∠4$.

Now, it can be obtained that:

$\begin{array}{l}∠1+∠2=∠3+∠4\\ ∠LMN=∠PNM\end{array}$

That implies,$∠LMNâ‰\dots ∠PNM$

In the triangles$â–³LMN$ and $â–³PNM$, the side that is common is $MN$.

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

As,$∠2â‰\dots ∠3$, thereforerole="math" localid="1648885940559" $∠PMNâ‰\dots ∠LNM$.

In the triangles $â–³LMN$ and $â–³PNM$, it can be noticed that$∠LMNâ‰\dots ∠PNM,\stackrel{¯}{MN}â‰\dots \stackrel{¯}{MN}$ and$∠PMNâ‰\dots ∠LNM$.

Therefore, the triangles $â–³LMN$and $â–³PNM$are the congruent triangles by using the $ASA$method.

The pair of overlapping triangles that are congruent are$â–³LMN$ and $â–³PNM$.

The triangles$â–³LMN$ and$â–³PNM$are congruent by the $ASA$method.