91Ó°ÊÓ

The given diagram is:

It is being given that $\stackrel{¯}{GH}âŠ\yen \stackrel{¯}{HJ}$,$\stackrel{¯}{KJ}âŠ\yen \stackrel{¯}{HJ}$and $\stackrel{¯}{GJ}â‰\dots \stackrel{¯}{KH}$.

As, $\stackrel{¯}{GH}âŠ\yen \stackrel{¯}{HJ}$, therefore by using the definition of perpendicular lines it can be said that $m∠GHJ=90°$.

As, $\stackrel{¯}{KJ}âŠ\yen \stackrel{¯}{HJ}$,therefore by using the definition of perpendicular lines it can be said that $m∠KJH=90°$.

Therefore, $m∠GHJ=m∠KJH=90°$.

Therefore, $∠GHJâ‰\dots ∠KJH$.

As, $\stackrel{¯}{GJ}â‰\dots \stackrel{¯}{KH}$, therefore,it can be noticedthat the hypotenuses of the triangles $â–\mu GHJ$ and $â–\mu KJH$ are equal.

In the triangles$â–\mu GHJ$ and $â–\mu KJH$, it can be noticed that the side $HJ$ is common.

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

As, $\stackrel{¯}{HJ}â‰\dots \stackrel{¯}{HJ}$, therefore, it can be noticed thatthe legs of the triangles$â–\mu GHJ$ and $â–\mu KJH$ are equal.

In the triangles $â–\mu GHJ$ and $â–\mu KJH$, it can be noticed that $\stackrel{¯}{GJ}â‰\dots \stackrel{¯}{KH}$ and $\stackrel{¯}{HJ}â‰\dots \stackrel{¯}{HJ}$.

Therefore, the triangles $â–\mu GHJ$ and $â–\mu KJH$ are congruent triangles by HL postulate.

The triangles $â–\mu GHJ$ and $â–\mu KJH$ are congruent triangles.

Therefore, by using the corresponding parts of congruent triangles it can be said that $\stackrel{¯}{GH}â‰\dots \stackrel{¯}{KJ}$.

The proof in two-column form is: