Answer:
Yes.
Explanation:
The SAS Theorem.
[I dunno if you can still see what I drew on there sorry if it is confusing]
If you visualize it, triangle HIK is the blue triangle, and triangle JIG is the green one. According to the diagram, the purple sides are congruent and the yellow ones are congruent. This means that segment IJ is congruent to segment IH, and segment IG is congruent to segment IK.
The two triangles also share an angle: angle GIK. This means that we can use the Side-Angle-Side Theorem to prove that the two triangles are congruent!
Hope this helps!