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One of the faces of a tetrahedron can be chosen arbitrarily, distinguished from the others and identified as the base of the tetrahedron.

In the above diagram, $ABC$ is the base of the tetrahedron $ABCD$.

As all faces of a tetrahedron are triangular by definition, it is qualitatively immaterial which face is thus chosen.

This definition is compatible with the definition of the base of a general pyramid.

Also see