Final answer:
By showing that FHG and KJG have two pairs of corresponding angles congruent, we can conclude that the two triangles are similar due to the AA (Angle-Angle) similarity criterion.
Step-by-step explanation:
To prove that triangles FHG and KJG are similar, we must demonstrate that they have the same shape, which can be established by showing that corresponding angles are equal and that the sides are proportional. Given that fh | gh and kj | gj, we know that FH // GH and KJ // GJ, where '//' denotes parallel lines. By the Alternate Interior Angle Theorem, this tells us that the angles formed by the intersection of these lines with a transversal must be equal. Thus, ∠FHG is congruent to ∠KJG, and ∠FGH is congruent to ∠KGJ.
Now, we can observe that triangles FHG and KJG share a common angle at point G, so we have two pairs of angles that are congruent, which by AA (Angle-Angle) criterion, proves that the triangles are similar. Since the triangles are similar, it follows that the ratios of their corresponding sides are equal. Hence, we can conclude that triangle FHG ∼ triangle KJG.