The best replacement for adjacent is contiguous.

The best alternatives to adjacent are rated as following:
★★★★★  contiguous
★★★★  adjoining
★★★★  adjacent to
★★★  vertical angles
★★  next to
★★  across
★  perpendicular
★  opposite
  abutting
  hypotenuse

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Speaking about adjacent, one probably shouldn't forget about angle and opposite.

Other search terms related to adjacent and their ratings are:
★★★★★ angle and opposite
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Google Trends

Scale is based on the average worldwide traffic of adjacent in all years. Click on graph for more.
adjacent
contiguous
adjoining