ileum, ilium

The words ileum, ilium sound the same but have different meanings and spellings. Why do ileum, ilium sound the same even though they are completely different words?

The answer is simple: ileum, ilium are homophones of the English language.

ileum
  1. :: noun

    The terminal portion of the small intestine extending from the jejunum to the cecum.

ilium
  1. ::

    See Troy.

Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.

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About Homophones

Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.

If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").