Prove is etymologically related to Be. Be is related to Beginning. Origin is a type of Beginning. Preliminary is a type of Origin. 
Boom is a type of Grow. Grow is related to Childhood. Childhood is a synonym of Minority. 
Prove --EtymologicallyRelatedTo--> Be <--RelatedTo--> Beginning <--IsA-- Origin <--IsA-- Preliminary 
Boom --IsA--> Grow <--RelatedTo--> Childhood <--Synonym--> Minority 