The question gives us a figure of a 4-sided shape and we are asked to find what condition would make triangle HMG and GKH congruent.
We shall go through each option to know if they provide the necessary condition for both triangles to be congruent.
Option 1:
< HMK = < GKH.
If this is true then we have the following:
From the above, Therefore, The two triangles cannot be congruent using SAS.
Option 2:
The two angles, equal, it means that the figure formed must be a square. But from all indications, we only know that line MG = line HK.
Therefore, the two triangles cannot be congruent on this option.
Option 3:
MG || HK.
This option makes MH parallel to GH. Since MG = HK from the question, it implies that MH = GH as well. Meaning that
this condition makes the figure a rectangle.
And by the alternate angles theorem,
Hence, from triangle HMG and triangle GKH, we have:
line GM = HK, line GH is common and
Hence, the final answer is Option 3