To show that two sides are congruent. Given information: ∠HGJ=∼∠KJG ∠KGJ=∼∠HJG

Formula used:
The below property is used:
Two triangles are congruent by ASA congruence rule.
Proof:
From figure, we get

It is given that,
${\displaystyle \mathrm{\angle }HGJ\stackrel{\sim }{=}\mathrm{\angle }KJG}$
${\displaystyle \mathrm{\angle }KGJ\stackrel{\sim }{=}\mathrm{\angle }HJG}$
By reflexive property, we get
${\displaystyle \overline{GJ}\stackrel{\sim }{=}\overline{GJ}}$
By ASA congruence rule, we get
${\displaystyle \mathrm{△}GHJ\stackrel{\sim }{=}\mathrm{△}JKG}$
As corresponding parts of congruent triangles are congruent, we get
${\displaystyle \overline{HG}\stackrel{\sim }{=}\overline{KJ}}$