The triangles ∆EGF and ∆JGH are similar by the Angle-Angle Similarity (AA~) criterion.
What is the Angle-Angle Similarity (AA~)?
Angle-Angle Similarity (AA~) states that if two angles in one triangle are congruent to two angles in another triangle, then the triangles are similar. In this case, angle H is congruent to angle F, and the common angle G is shared by both triangles. Therefore, the triangles ∆EGF and ∆JGH satisfy the AA~ criterion, establishing their similarity.
Hence, based on the Angle-Angle Similarity criterion, we can conclude that the triangles ∆EGF and ∆JGH are indeed similar. The congruence of angles H and F, along with the shared angle G, establishes the similarity relationship between the two triangles.