gage, gauge

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

The answer is simple: gage, gauge are homophones of the English language.

gage
  1. :: noun

    Something deposited or given as security against an obligation; a pledge.

  2. :: noun

    Something, such as a glove, that is offered or thrown down as a pledge or challenge to fight.

  3. :: noun

    A challenge.

  4. :: verb-transitive

    Archaic To pledge as security.

gauge
  1. :: noun

    A standard or scale of measurement.

  2. :: noun

    A standard dimension, quantity, or capacity.

  3. :: noun

    An instrument for measuring or testing.

  4. :: noun

    A means of estimating or evaluating; a test: a gauge of character. See Synonyms at standard.

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").