The Spanish verb 'alegrar' (meaning 'to make happy') comes from the Latin word 'alacer', which meant 'lively' or 'animated'. This Latin word first evolved into the Spanish adjective 'alegre' (meaning 'happy' or 'joyful'). Then, by adding the verbal prefix 'a-' and the infinitive suffix '-ar' to 'alegre', the verb 'alegrar' was formed, giving it the causative meaning of 'to make happy' or 'to cheer up'.

This pattern of forming verbs by adding 'a-' and '-ar' to adjectives is common in Spanish, where the resulting verb often means 'to make (something/someone) [adjective]'.

The most obvious related Spanish word is the adjective 'alegre', which means 'happy' or 'joyful'. This is actually the base word from which 'alegrar' was formed. You might also encounter 'alegría' (happiness, joy), which is a noun derived from the same root. These words form a family sharing the core meaning of happiness and joy.

While there aren't any common English words directly related to 'alegrar', the Latin root 'alacer' did give us some less common English words like 'alacrity', which means 'cheerful readiness, promptness, or willingness'. You can see how the original meaning of 'lively, animated' in Latin evolved slightly differently in English and Spanish, with Spanish focusing more on the emotional aspect of joy and happiness, while English preserved more of the 'eager readiness' sense in 'alacrity'.