The words pique, peak, peek, peke sound the same but have different meanings and spellings. Why do pique, peak, peek, peke sound the same even though they are completely different words?
The answer is simple: pique, peak, peek, peke are homophones of the English language.
A tapering, projecting point; a pointed extremity: the peak of a cap; the peak of a roof.
The pointed summit of a mountain.
The mountain itself.
The point of a beard.
To glance quickly.
To look or peer furtively, as from a place of concealment.
To be only partially visible, as if peering or emerging from hiding: Tiny crocuses peeked through the snow.
A brief or furtive look.
A state of vexation caused by a perceived slight or indignity; a feeling of wounded pride.
To cause to feel resentment or indignation.
To provoke; arouse: The portrait piqued her curiosity.
To pride (oneself): He piqued himself on his stylish attire.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from the GNU version of the Collaborative International Dictionary of English and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.