91Ó°ÊÓ

As$\stackrel{¯}{JL}âŠ\yen Z$ implies that$\stackrel{¯}{JL}âŠ\yen \stackrel{¯}{KN}$ and $\stackrel{¯}{JL}âŠ\yen \stackrel{¯}{KM}$. Therefore,$m∠JKN=90$ and $m∠JKM=90$.

Consider $\mathrm{Δ}JKM$and $\mathrm{Δ}JKN$in which, $\stackrel{¯}{KM}â‰\dots \stackrel{¯}{KN}$, $∠JKNâ‰\dots ∠JKM$and $\stackrel{¯}{JK}â‰\dots \stackrel{¯}{JK}$ then by SAS postulate $\text{Δ}JKMâ‰\dots \text{Δ}JKN$.

As $\mathrm{Δ}JKMâ‰\dots \mathrm{Δ}JKN$, by corresponding parts of congruent triangles, $\stackrel{¯}{JM}â‰\dots \stackrel{¯}{JN}$.

If the two sides of a triangle are equal in length, then it is an isosceles triangle.

Here,$\stackrel{¯}{JM}â‰\dots \stackrel{¯}{JN}$ implies that$\mathrm{Δ}JMN$ is an isosceles triangle.

As$\stackrel{¯}{JL}âŠ\yen Z$ implies that$\stackrel{¯}{JL}âŠ\yen \stackrel{¯}{KN}$ and $\stackrel{¯}{JL}âŠ\yen \stackrel{¯}{KM}$. Therefore,$m∠LKN=90$ and $m∠LKM=90$.

Consider$\mathrm{Δ}LKM$ and$\mathrm{Δ}LKN$ in which, $\stackrel{¯}{KM}â‰\dots \stackrel{¯}{KN}$,$∠LKNâ‰\dots ∠LKM$ and$\stackrel{¯}{LK}â‰\dots \stackrel{¯}{LK}$ then by SAS postulate $\mathrm{Δ}LKMâ‰\dots \mathrm{Δ}LKN$.

As $\mathrm{Δ}LKMâ‰\dots \mathrm{Δ}LKN$, by corresponding parts of congruent triangles, $\stackrel{¯}{LM}â‰\dots \stackrel{¯}{LN}$.

If the two sides of a triangle are equal in length, then it is an isosceles triangle.

Here,$\stackrel{¯}{LM}â‰\dots \stackrel{¯}{LN}$ implies that$\mathrm{Δ}LMN$ is an isosceles triangle.

Therefore,$\mathrm{Δ}JMN$ and$\mathrm{Δ}LMN$ are an isosceles triangle.

If the two sides of a triangles are congruent then the angle opposite to those sides are congruent.

The two triangles will be congruent only if$\stackrel{¯}{JK}â‰\dots \stackrel{¯}{LK}$.

Therefore, the two isosceles triangles must not be congruent.