Answer:
See proof below
Explanation:
We will use the SAS condition for congruency of two triangles
SAS (Side-Angle-Side)
If any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.
In the two triangles ΔHIK and ΔJIK we have
m∠4 = m∠3 (given)
HK ≅ KJ
IK is the common side
So the two sides HK and IK are equal and the included angles ∠4 and ∠3 are also equal
So by SAS, the two triangles are equal
So m∠2 = m∠1
which means IK bisects ∠HIK